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

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340 Principles of Radiation Interaction in Matter and Detection

where R

is the proton rigidity at the same kinetic energy, i.e., E

k,p

= E

. In

addition, it can be remarked that for the stable

∗∗

and most abundant isotopes in

the heliosphere [i.e., up to nickel (Sect. 4.1.2.4)]

isot

≈ 2.0–2.3.

As a consequence, less energetic (but heavier than proton) PCRs can penetrate

deeply the magnetosphere: in any location, the associated geomagnetic cut-oﬀ rigi-

dity, R

cut

, requires a kinetic energy of the isotope lower than that of a proton [see

Eq. (4.68)]. As discussed in [Bobik et al. (2006)], the rigidity (R

cut

) of geomagnetic

cut-oﬀ varies as a function of the observation location and increases with decreas-

ing the geomagnetic latitude: the PCRs with rigidities lower than the local value

of R

cut

cannot reach that observation region.

This eﬀect is visible in Fig. 4.12(a), which, at the magnetosphere boundary (i.e.,

at 1 AU), shows the spectra (indicated as “cosmic”) of the i) proton and helium

diﬀerential energy distributions observed using the AMS-01 spectrometer and ii)

carbon and iron observed using the HEAO-3-C2 spectrometer (see also [Bobik et

al. (2006b); Boella et al. (2008)]). Figure 4.12(a) also shows the proton (helium)

spectrum observed with the AMS-01 spectrometer at the Shuttle altitude in the

geomagnetic region 0.3 ≤ |Θ

| ≤ 0.4 (0 ≤ |Θ

| ≤ 0.4). In Fig. 4.12(b), the same

spectra are shown as function of the particle rigidity expressed in GV. The AMS-

01 observations were carried out in June 1998 during the solar cycle 23; HEAO-3

observations from October 1979 up to June 1980, i.e., during the solar cycle 21. In

both periods the solar activity was rising from the minimum to the subsequent

maximum and the solar magnetic ﬁeld polarity was positive. The angular acceptance

of the detectors, the altitude and the inclination of the orbits were such that the

observations were obtained under not too diﬀerent experimental conditions. For

instance, for 0 ≤ |Θ

| ≤ 0.4 the geomagnetic cut-oﬀ rigidity is similar for protons

and helium particles [Fig. 4.12(b)], but it aﬀects energetic protons more than helium

particles [e.g., see the cut-oﬀ eﬀect shown in Fig. 4.12(a)].

At 1 AU and outside the Earth’s magnetosphere, the relative abundances to

protons for He (He/p), C (C/p) and Fe (Fe/p) nuclei can be calculated using the

“cosmic”-data (Fig. 4.12(a)); above 0.8 GeV/nucleon, the relative abundances

are

cos

He/p

≈ 0.067, <

cos

C/p

≈ 0.0019 and <

cos

fe/p

≈ 0.00018

for He/p, C/p and Fe/p, respectively [Gervasi and Grandi (2008)]. Furthermore

at an altitude of 400 km, the relative abundances inside the magnetosphere and

∗∗

For

H (tritium) and

He, this ratio is 3 and 1.5, respectively. Tritium has several diﬀerent

experimentally-determined values of its half-life, the recommended value (e.g., see the web site:

http://nvl.nist.gov/pub/nistpubs/jres/105/4/j54luc2.pdf ) is 4500 ± 8 days (approximately 12.32

years). It decays into

He [Eq. (3.21)] by the reaction

H →

He + e

−

+ ¯ν

These values are aﬀected by the solar modulation and may diﬀer from those which are derived

using abundances at ﬁxed values of kinetic energy per nucleon, large enough so that particles are

marginally modulated (e.g., see Fig. 4.11).

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Radiation Environments and Damage in Silicon Semiconductors 341

Fig. 4.12 Proton [AMS Collab. (2000a,d)], He [AMS Collab. (2000b)], C [Engelmann et al.

(1990)] and Fe [Engelmann et al. (1990)] ﬂuxes as functions of (a) kinetic energy per nucleon

in GeV/nucleon and (b) particle rigidity in GV: p (•), He (¥), C (F) and Fe (¨) cosmic (i.e.,

these ﬂuxes are observed well above the geomagnetic cut-oﬀ and can be considered at about 1

AU), p (N) in the geomagnetic region 0.3 ≤ |Θ

| ≤ 0.4 and He (H) in the geomagnetic region

0 ≤ |Θ

| ≤ 0.4 (from [Leroy and Rancoita (2007)]). At |Θ

| ≈ 0.4, R

cut

(the associated geomag-

netic cut-oﬀ proton rigidity) is ≈ 7–8 GV.

their ratios with those outside at 1 AU (i.e., the enhancement factors E

’s) were

computed using a transmission function (TF) approach (e.g., see [Boella et al.

(2008)] and discussion at page 342): for geomagnetic latitudes ranging from ≈ −46

◦

up to ≈ 46

◦

, the values of E

’s depend on the mass number I

isot

and are

∗

2.06 . E

. 3.74.

∗

See the discussion in Bobik, P. et al. (2009), Fluxes and Nuclear Abundances of Cosmic Rays in-

side the Magnetosphere using a TF Approach, J. Adv. Space Res., doi: 10.1016/j.asr.2008.11.020.

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342 Principles of Radiation Interaction in Matter and Detection

Thus, the resulting magnetospheric isotopic relative-abundances i) are modiﬁed be-

cause the proton component is more depleted than the other isotopic components

of GCR’s and ii) can depend on parameters like the geomagnetic latitude and/or

altitude.

It has to be noted that in Fig. 4.12 the proton (for 0.3 ≤ |Θ

| ≤ 0.4) and He (for

0 ≤ |Θ

| ≤ 0.4) spectra include both primary and secondary cosmic rays. These

latter are responsible for the ﬂux increase below R

cut

. In addition, the same eﬀect

is visible in the diﬀerential energy spectra for H, He and Fe for one solar cycle from

minimum to maximum reported in [Smart and Shea (1989); Gabriel (2000)].

As previously mentioned, in [Bobik et al. (2006)] the passage of the primary

protons through the magnetosphere to the AMS-01 spectrometer was treated using

the so-called transmission function [Adams et al. (1991); Boberg et al. (1995)],

which was determined by back-tracking the proton trajectories to determine those

allowed to primaries: the access of a primary proton to the observation location

is supposed to be allowed when the back-tracked particle trajectory reaches the

magnetopause. The TFs allowed one [Bobik et al. (2006)] to untangle the spec-

tra due to secondary protons from those observed, as function of the geomagne-

tic latitude, using the primary proton spectrum at 1 AU (the “cosmic”-protons in

Fig. 4.12). Some SCRs (mostly re-entrant albedo protons) were also found to pop-

ulate the rigidity regions above the local rigidity of geomagnetic cut-oﬀ [Bobik et

al. (2006)].

4.1.3 Neutron Spectral Fluence in Nuclear Reactor Environment

In the phenomenon of the neutron-induced nuclear ﬁssion, a nucleus captures a

neutron and breaks up into two nuclei (e.g., see Sections 5.2 and 5.5 in [Byrne

(1994)]). This process is accompanied by a large release of energy, typically about

200 MeV/ﬁssion, and the emission of one or more fast neutrons. A controlled self-

sustaining chain of ﬁssion reactions is called chain-reacting pile or nuclear reac-

tor. The ﬁrst reactor was built by Fermi in 1942. The modern nuclear reactors are

basically machines that contain and control nuclear ﬁssion reactions, while pro-

ducing electricity. Besides power reactors, there are research reactors (like TRIGA

and Godiya types and others, see for instance [Kelly, Luera, Posey and Williams

(1988)], Chapter 5 in [Messenger and Ash (1992)] and [Angelescu et al. (1994)]),

which can provide sources of ﬁssion neutrons, for testing the performance of VLSI

transistors (and circuits) and detectors, and allow the simulation of nuclear environ-

ments (e.g., nuclear power reactors and weapons or high-luminosity colliding beam

accelerators).

The kinetic energies (E) of reactor ﬁssion neutrons do not exceed ≈

15 MeV. However, the available ﬁssion spectra diﬀer for the energy distribution

of both thermal and fast neutrons (Table 4.2) and are characterized by a neutron

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Radiation Environments and Damage in Silicon Semiconductors 343

spectral-ﬂuence φ(E) in n/(cm

MeV) obtained as

φ(E) =

ψ(E, t) dt, (4.77)

where ψ(E, t) is the neutron spectral-ﬂux in n/(s cm

MeV), and by a neutron ﬂuence

min

φ(E) dE [n/cm

], (4.78)

where E

min

is the minimum neutron kinetic-energy (typically about 10 keV) to

induce radiation damage by atomic displacements (see for instance Section 5.9

in [Messenger and Ash (1992)]). Thus, Φ

accounts for the neutron ﬂuence

‡‡

re-

lated to radiation-induced damages, i.e., above 10 keV in n–silicon interactions, the

energy released for displacement damages is no longer negligible (see Sect. 4.2.1).

The displacement damages induced by neutrons can be normalized to displa-

cement damages induced by 1 MeV neutrons by means of the hardness parameter

(κ) also termed hardness factor (see Sect. 4.2.1 and, for a further discussion, see

for instance [Namenson, Wolicki and Messenger (1982); Kelly, Luera, Posey and

Williams (1988); Vasilescu (1997)]). For ﬁssion neutrons with spectral ﬂuence φ(E),

the 1 MeV equivalent neutron ﬂuence is given by:

1 MeV

= κ

min

φ(E) dE = κ Φ

. (4.79)

1 MeV

is the ﬂuence of 1 MeV neutron needed for generating the same amount of

displacement damage compared to the ﬁssion ﬂuence Φ

(see, also, footnote at page

291).

4.1.3.1 Fast Neutron Cross Section on Silicon

Neutron interactions on nuclei were widely studied and their cross sections deter-

mined exp erimentally: these latter are, for instance, available on the web at the

IAEA

- Nuclear Data Service (2007).

In addition, nowadays, for the scattering of a fast neutron on

Si a systematic

evaluation of all important cross sections is reported in [Tagesen, Vonach and Wall-

ner (2002)]: it covers the neutron energy-range (1.75–20) MeV, i.e., for an energy

range well above the resonance region (Sect. 4.1.3.2) and of interest for reactions

resulting in displacement damage. The evaluation uses experimental data compiled

in EXFOR (e.g., see [IAEA - Nuclear Data Service (2007)]) supplemented by very

recent ones: the total and elastic cross sections are shown in Fig. 4.13. The elastic

cross section was obtained as the diﬀerence between the total and non-elastic cross

sections. This latter was derived summing the inelastic cross sections and those for

reactions like, for example, (n,2n), (n,p), (n,α), (n,d). . . (for a complete discussion

see [Tagesen, Vonach and Wallner (2002)] ).

‡‡

The total neutron ﬂuence can be computed with E

min

= 0.

IAEA is the International Atomic Energy Agency located in Vienna (Austria).

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344 Principles of Radiation Interaction in Matter and Detection

Fig. 4.13 Total and elastic (see text) cross sections (in barn) for neutrons on

Si with kinetic energies of (1.75–20) MeV. The lines are to guide the

eye. Data were obtained from [Tagesen, Vonach and Wallner (2002)].

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Radiation Environments and Damage in Silicon Semiconductors 345

Table 4.2 Classiﬁcation of neutrons as a function of kinetic energy.

Energy Classiﬁcation and Subdivision Subdivision energy-range

(eV) E

(eV)

0 < E

< 1 Slow











Ultra cold

Very cold

Cold

Thermal

Epithermal

< 2 × 10

−7

2 × 10

−7

≤ E

< 5 × 10

−5

5 × 10

−5

≤ E

. 0.025

' 0.025

0.025 . E

≤ 1

1 < E

< 10

Intermediate







including

Resonance 1 < E

< 100

< E

< 10

Fast

(1)

< E

< 5 × 10

Very fast

5 × 10

< E

< 10

Ultra fast

> 10

Relativistic

(1)

: in Section 1.5.5.3 of [Byrne (1994)], a neutron with kinetic energy > 1 MeV is termed fast; in

Section 12.2.2 of [Marmier and Sheldon (1970)], a neutron is considered fast for 0.5 < E

< 10 MeV.

4.1.3.2 Energy Distribution of Reactor Neutrons and Classiﬁcation

As mentioned in the previous section, reactor-neutron production is one of the most

widely used methods of obtaining fast neutrons. The spectral ﬂuence of emerging

almost-thermal and fast neutrons depends on the type of reactor and moderator

(e.g., see Chapter 12 of [Marmier and Sheldon (1970)], [Kelly, Luera, Posey and

Williams (1988)], Chapter 5 in [Messenger and Ash (1992)], Chapter 1 of [Byrne

(1994)] and [Angelescu et al. (1994)]). The spectral ﬂuence largely decreases with

increasing energy and, usually, it has a high-energy tail which extends up to energies

above 10–15 MeV.

Neutrons are classiﬁed as a function of their kinetic energy. However, the clas-

siﬁcation has slightly varied with time. Commonly used terms, their subdivisions

and kinetic energy ranges are shown in Table 4.2, following the classiﬁcation i) for

slow (≤ 1 eV), intermediate (1 eV–1 MeV) and fast (> 1 MeV) neutrons from Sec-

tion 1.5.5.3 of [Byrne (1994)] and ii) above 10 MeV from Section 12.2.2 of [Marmier

and Sheldon (1970)]. The energy of 1 eV

is chosen to deﬁne the energy below

which a neutron is termed slow. By convention, a thermal neutron is taken to have

an energy of 0.025 eV. This energy is the mean energy of a neutron at thermal

equilibrium with its surrounding at 20

◦

C; it corresponds to a neutron velocity of

' 2.2 km/s and a neutron wavelength of ' 1.8

In silicon, displacement damage is mostly induced by fast, very fast, ultra fast

It is the typical energy of the lowest resonance in the reactor moderating material (e.g., see

Section 1.5.5.3 of [Byrne (1994)]).

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346 Principles of Radiation Interaction in Matter and Detection

and relativistic neutrons (see Sects. 4.2.1, 4.2.1.2 and 4.2.1.5). In this book, the

term fast neutron is commonly used for a neutron i) with kinetic energy lower than

that corresponding to the ultra fast region and ii) capable to induce a relevant

displacement damage (e.g., see Figs. 4.18 and 4.19), thus, typically with kinetic

energies & 10 keV (e.g., see Sects. 4.1.3 and 4.2.1). Furthermore, it has to be noted

that the damage induced by a 1 MeV neutron is taken as ASTM-standard reference

[ASTM (1985)] (see Sect. 4.2.1).

4.2 Relevant Processes of Energy Deposition and Damage

Particles and photons passing through matter lose energy (or can be absorbed) by

means of a variety of interactions and scattering processes, which result in two major

eﬀects: the collision energy-loss and atomic displacement. Interactions

of incoming

particles which result in the excitation or emission of atomic electrons (i.e. ionizing

the atom) are referred to as energy-loss by ionization or energy-loss by collisions

(see Sect. 4.2.3). The non-ionization energy-loss (NIEL) processes are interactions in

which the energy imparted by the incoming particle results in atomic displacements

or in collisions where the knock-on atom does not move from its lattice location and

the energy is dissipated in lattice vibrations (phonons), for instance.

The energy deposition by non-ionization processes is much lower (except for

neutrons) than that by ionization. However, bulk damage mechanisms result mostly

from atomic displacements (the so-called displacement damages).

Although the mechanisms of induced damage are somewhat similar in semicon-

ductors and in semiconductor components, we restrict this treatment to what is

relevant for silicon radiation-detectors and devices.

4.2.1 NIEL and Displacement Damage

Displacements occur when the primary interaction results in the displacement of

the recoil atom from its lattice position. The knock-on atoms (PKAs) primarily

create Frenkel defects (called also Frenkel-pairs; see, for instance, [James and Lark-

Horovitz (1951); Kraner (1982)]). A Frenkel defect, which diﬀers from dislocations

and more complex imp erfections, is a pair of point defects (i.e., highly localized

imperfections arising in a crystal from a one-atom disorder) close enough to exhibit

an interaction: a vacancy (V ) and an atom in interstitial position (I).

For collisions hard enough to allow large energy transfers, the PKA can collide

with other lattice atoms, creating more vacancies and interstitial atoms. At thermal

equilibrium, the recoil atoms will be located in interstitial positions, unless some

of them recombine with vacancies: some of these point defects are isolated, but for

These interactions in matter are reviewed in the chapter on Electromagnetic Interaction of

Radiation in Matter with an extensive treatment of collision energy-losses in silicon media (see,

also, Chapter 2 in [Leroy and Rancoita (2004)]).

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Radiation Environments and Damage in Silicon Semiconductors 347

recoil energies much larger than the displacement threshold energy, E

, cascading

displacements will occur in a closely spaced group of defects (the so-called cluster

or cluster of defects, e.g., see Sect. 4.2.2) within a small spatial region (or even a

few small spatial regions). Figure 4.14 shows an example of simulated cascading-

displacements by a silicon recoil in bulk silicon after the interaction with an incoming

neutron of 50 keV kinetic energy (from [van Lint, Leadon and Colweel (1972)]; see

also Chapter 2 of [van Lint, Flanahan, Leadon, Naber and Rogers (1980)]): a

few energetic collisions produce other energetic recoils interspaced with many more

low-energy transfers. Thus, cascading displacements result in (terminal) clusters of

defects.

The thermal energy allows some defects to migrate through the crystal and,

eventually, be annihilated by the recombination of the V –I pairs or create stable

defects in association with other impurities or defects already present (or induced

by radiation). The presence of defects and clusters of defects produces changes in

the properties of the semiconductor.

In radiation-induced defects, E

is several times greater than the energy re-

quired for adiabatic displacements of atoms from lattice to interstitial positions. E

depends on the recoil direction and, for silicon, is about (13–33) eV (e.g., see Chap-

ter 1 in [Vavilov and Ukhin (1977)], [Chilingarov, Lipka, Meyer and Sloan (2000)]

and references therein). In most of calculations, in particular for incoming neutrons

(see Sect. 4.2.1.5), an isotropic value of 25 eV is assumed (e.g., see page 24 of [Di-

enes and Vineyard (1957)], Section 2.4.2 in [van Lint, Flanahan, Leadon, Naber and

Rogers (1980)] and references therein, see also Section V of [Nichols and van Lint

(1966)]).

There has b een substantial progress in understanding the degradation generated

in integrated bipolar transistors

and silicon detectors

by fast neutrons, i.e., typ-

ically above 10 keV, which induce displacement damages. Neutrons with suﬃcient

large energies, like for instance fast neutrons, can transfer enough kinetic energy to

the recoil atom to generate clusters of displacements with a cascading eﬀect.

Most predictions of the neutron energy dependence in semiconductor (i.e. sili-

con) devices have been based on the amount of non-ionizing energy deposited. In

literature (see for instance [Namenson, Wolicki and Messenger (1982); Ougouag,

Williams, Danjaji, Yang and Meason (1990); Vasilescu (1997)]), the damage eﬀect

due to initial and cascading-displacements induced by neutrons (Sect. 4.2.1.2) is

The reader can see, e.g., [Messenger (1966, 1972, 1992); Colder et al. (2001); Claeys and Simoen

(2002); Holmes-Siedle and Adams (2002); Co degoni et al. (2004b); Consolandi, D’Angelo, Fallica,

Mangoni, Modica, Pensotti and Rancoita (2006)] and references therein.

One can see, e.g., [Borgeaud, McEwen, Rancoita and Seidman (1983); SICAPO Collab. (1986,

1994b,c, 1995c); Croitoru, Dahan, Rancoita, Rattaggi, Rossi and Seidman (1997); Croitoru, Ran-

coita, Rattaggi, Rossi and Seidman (1997); Dezillie, Bates, Glaser, Lemeilleur and Leroy (1997);

Borchi, Bruzzi, Leroy, Pirollo and Sciortino (1998); Croitoru, David, Rancoita, Rattaggi and Sei-

dman (1998a); Croitoru, Gubbini, Rancoita, Rattaggi and Seidman (1999a); Leroy, Roy, Casse,

Glaser, Grigoriev and Lemeilleur (1999a); Mangiagalli, Levalois, Marie, Rancoita and Rattaggi

(1999); Golan et al. (2001); Rose Collab. (2001)] and references therein.

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348 Principles of Radiation Interaction in Matter and Detection

expressed by the damage function (also referred to as displacement kerma func-

tion) D(E) in units of MeV cm

, whose value at 1 MeV is the ASTM standard

D(1 MeV) = 95 MeV mb [ASTM (1985)]. The damage function

∗∗

, which accounts

for both the cross section for neutron–silicon scattering and the energy released in

creating displacements, is given by [Codegoni et al. (2004b); Consolandi, D’Angelo,

Fallica, Mangoni, Modica, Pensotti and Rancoita (2006)]:

D(E) =

(E)

(E, E

) dE

, (4.80)

where E is the incoming neutron kinetic-energy, σ

(E) is the cross section for the

k-th reaction, f

(E, E

) dE

is the probability that a recoil atom is generated with

kinetic energy between E

and E

+ dE

, and, ﬁnally, P

) is the partition

energy for the recoil nucleus. This latter is the part of the recoil energy deposited

in displacements, calculated in the framework of the Lindhard screened-potential

scattering theory [Lindhard, Nielsen, Scharﬀ and Thomsen (1963)], based on the

Thomas–Fermi model and further developments [Parkin and Coulter (1977, 1979);

Coulter and Parkin (1980)], or, for instance, by means of Robinson’s analytical

approximation [Robinson (1970)] (e.g., for elastic neutron–silicon interactions see

Eq. (4.90) for silicon recoil in a silicon medium). The damage function for neutron

is reviewed in Sect. 4.2.1.5.

From Equation (4.80), the energy density, E

dis

, deposited through atomic

displacements by neutrons characterized by a neutron spectral-ﬂuence φ(E) in

n cm

−2

MeV

−1

(Sect. 4.1.3), is the damage energy, E

, (i.e., the defect producing

energy) imparted per cm

and is given by:

dis

= n

min

D(E) φ(E) dE [MeV/cm

], (4.81)

where [see page 14 and Eq. (1.39)]

(4.82)

is the number of atoms per cm

in the bulk silicon, ρ

and A

are the density and

atomic weight of the silicon medium, respectively; N is the Avogadro constant (see

Appendix A.2) and E

min

is the minimum neutron energy for inducing displacement

damage. Since the damage function for soft and thermal neutron is much lower

than that for fast neutrons (Sect. 4.2.1.5), for spectral ﬂuences of reactor neutrons

the integral in Eq. (4.81), thus the value of E

dis

, marginally depends on E

min

to about 10 keV. For example, in the case of the neutron spectrum of the Triga

reactor RC:1 at Casaccia (Rome) the value of E

dis

varies by no more than 0.5% for

min

≤ 10 keV [Codegoni et al. (2004b); Consolandi, D’Angelo, Fallica, Mangoni,

Modica, Pensotti and Rancoita (2006)].

∗∗

See, for instance, [Ougouag, Williams, Danjaji, Yang and Meason (1990)] and Chapter 5 in

[Messenger and Ash (1992)].

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Radiation Environments and Damage in Silicon Semiconductors 349

Fig. 4.14 Simulation of cascading-displacements generated by a silicon recoil in bulk silicon after

the interaction with an incoming neutron of 50 keV kinetic energy (adapted and reprinted with

permission from van Lint, V.A.J., Leadon, R.E., and Colwell, J.F., Energy Dependence of Di-

splacement Eﬀects in Semiconductors, IEEE Transactions on Nuclear Science, Volume 19, Issue

6, Dec. 1972, pages 181–185, doi: 10.1109/TNS.1972.4326830,

° 1972 IEEE; see also Chapter 2

of [van Lint, Flanahan, Leadon, Naber and Rogers (1980)]). The distances are in

The concentration of Frenkel-pairs (FP ), i.e., the number of Frenkel defects per

, can be computed by means of the modiﬁed Kinchin–Pease formula [Eq. (4.89),

see also discussion in Sect. 4.2.1.1] and Eq. (4.81) as:

FP ∼

dis

2.5 E

. (4.83)

For the case of the Triga neutron spectrum Eq. (4.83) yields a Frenkel-pairs concen-

tration of about 43.3 per incoming neutron per cm

with energy above 10 keV. This

value also accounts for the low energy part of the neutron spectrum, i.e., below

10 keV, which contributes by no more than 0.5% to the FP overall value.

From Eqs. (4.79, 4.81), we can derive the hardness parameter κ as:

D(1 MeV) Φ

1 MeV

= κ n

D(1 MeV)

min

φ(E) dE

= n

min

D(E) φ(E) dE,