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

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530 Principles of Radiation Interaction in Matter and Detection

Table 6.5 Theoretical hardness factors computed from

the displacement damage function D(E) normalized to the

1 MeV neutrons value (from [Leroy and Rancoita (2007)]).

Particle κ

theo

[D(E)/95 MeV mb]

1 MeV neutrons 1.00

7 MeV protons 7.40

8 MeV protons 5.90

9 MeV protons 5.10

10 MeV protons 4.50

∗

24 GeV/c protons 0.62

∗

The value for the 24 GeV/c protons is an experimental

value extracted from [Rose Collab. (2001)].

re-normalized to 20

◦

C [Sze (1981)]. By re-writing Eq. (4.134) [see Sect. 4.3.2],

the leakage current per unit volume (I

vol

) as a function of ﬂuence (Φ) is given

by (e.g., [Kraner, Li and Posnecker (1989)]):

vol

(Φ) − I

v ol

(0) = α Φ, (6.161)

where α is the radiation-induced reverse current damage constant [in Eq. (4.134),

v ol

(Φ) = I

r,irr

v ol

and I

vol

(0) = I

vol

]. It is found [Bechevet, Glaser, Houdayer,

Lebel, Leroy, Moll and Roy (2002)] that the values of the α parameter extracted

after heating the detectors for 4 minutes at 80

◦

C show good agreement between SP

and PM detectors.

The irradiation induced change on the α parameter as a function of the heating

temperature (T

) and heating time (t) for detectors (guard ring connected) is given

by the phenomenological expression [Moll (1999)]:

t/T

= α

exp

−

+ α

− β ln

. (6.162)

Equation (6.162) is a convenient parametrization which does not pretend to be

based on a physical model [Moll (1999)]. Fitting Eq. (6.162) to the experimental

data [Bechevet, Glaser, Houdayer, Lebel, Leroy, Moll and Roy (2002)], one can see

that the decrease of the leakage current with annealing is more signiﬁcant for the

SP detectors as compared to the PM detectors.

In summary, the results of PM detectors studies show that detectors produced

by planar MESA technology have a satisfactory performance as particle detectors

operated in high radiation environment. MESA planar silicon detectors were ex-

posed to low energy protons in order to extract the evolution of the eﬀective dop-

ing concentration and leakage current as a function of ﬂuence, up to a ﬂuence of

5×10

p cm

−2

. The detectors have been heated at 80

◦

C in order to study the ageing

of the detectors. Altogether, the behavior under irradiation of PM and SP detectors

is comparable, though the decrease of the leakage current with annealing is more

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Solid State Detectors 531

-2

-1

1 10 10

7 MeV

8 MeV

9 MeV

10 MeV

24 GeV/c

Proton fluence (10

p cm

-2

)

Leakage current (µA/cm

)

Fig. 6.46 The leakage current (in µA/cm

) as a function of the proton ﬂuence (Φ in units of

p cm

−2

) after heating for 4 minutes at 80

◦

C (reprinted from Nucl. Instr. and Meth. in

Phys. Res. A 479, Bechevet, D., Glaser, M., Houdayer, A., Lebel, C., Leroy, C., Moll, M. and

Roy, P., Results of irradiation tests on standard planar silicon detectors with 7–10 MeV protons,

487–497, Copyright (2002), with permission from Elsevier).

signiﬁcant for the SP detectors, particularly after inversion. Measurements of the

charge collection eﬃciency (CCE) as a function of ﬂuence were performed [Chren

et al. (2001)]. At a ﬂuence Φ ≈ 10

particles cm

−2

, the charge carrier lifetime

degradation due to trapping with increased ﬂuence is responsible for a charge col-

lection deﬁcit of about 12% and about 10% for β-particles incident on MESA and

standard planar detectors, respectively. For α-particles incident on the front side,

one ﬁnds a deﬁcit of 20% for MESA and 25% for standard planar detectors. The

deﬁcit increases to 30% and 35% for α-particles incident on the back side of MESA

and SP detectors, respectively. These results are in good agreement with existing

direct measurements ([Casse et al. (1999a); Leroy et al. (1994)], see also [SICAPO

Collab. (1994b,c)]).

6.8.3 Irradiation with Low-Energy Protons and Violation of NIEL

Scaling in High-Resistivity Silicon detectors

Standard planar silicon detectors were exposed [Bechevet, Glaser, Houdayer, Lebel,

Leroy, Moll and Roy (2002)] to low-energy protons in order to extract the evolution

of the eﬀective doping concentration and leakage current as a function of ﬂuence,

up to a ﬂuence of 7 × 10

p/cm

. These measurements were part of a study done

for the LHC. The radiation hardness of standard planar silicon detectors exposed

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532 Principles of Radiation Interaction in Matter and Detection

-2

-1

1 10 10

7 MeV

8 MeV

9 MeV

10 MeV

24 GeV/c

(10

p cm

-2

)

Leakage current (µA/cm

)

Fig. 6.47 The leakage current (in µA/cm

) as a function of 1 MeV neutron equivalent ﬂuence

(Φ

= Φ ×κ

in units of 10

p cm

−2

) after heating for 4 minutes at 80

◦

C (reprinted from Nucl.

Instr. and Meth. in Phys. Res. A 479, Bechevet, D., Glaser, M., Houdayer, A., Lebel, C., Leroy,

C., Moll, M. and Roy, P., Results of irradiation tests on standard planar silicon detectors with

7–10 MeV protons, 487–497, Copyright (2002), with permission from Elsevier).

to low-energy protons was tested and the results were compared to those obtained

from the irradiation of similar material with 24 GeV/c protons. The goal of this

study was also to understand the limits of NIEL scaling and therefore the limits for

predictions of radiation damage produced by protons with diﬀerent energies. The

resistivity of the detectors used for the study was 2 kΩcm and the proton energies

used were 7, 8, 9, 10 MeV. No proton of energy lower than 7 MeV was used to be

sure that these protons were not stopped in the 300 µm (295 ±5 µm) thick detectors

(Table 6.4 and [Berger, Coursey, Zucker and Chang (2005)]).

Since the LHC experiments will be in operation for at least 10 years, it is nec-

essary to study the long term behavior of silicon detectors to be used in these

experiments when exposed to high level of radiations.

The detectors were heated at 80

◦

C for up to 17 hours in order to extract the

damage parameters necessary to simulate the detectors ageing during 10 years of

operation of the LHC experiments. A word of explanation is needed to understand

the choice of the temperature of 80

◦

C. Heating detectors after their irradiation

has become a standard procedure. This procedure allows the comparison of particle

irradiations without the inﬂuence of the irradiation time and the samples irradiated

at diﬀerent facilities can be considered as being in the same annealing state. The

eﬀective doping concentration, N

eﬀ

, varies with the diode ageing. At ﬁrst, N

eﬀ

(and

then V

) decreases with time after being heated. This period of beneﬁcial annealing

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Solid State Detectors 533

Table 6.6 Value of the parameter α and of the hardness factor κ

extracted from the leakage current as a function of the proton ﬂuence

(Fig. 6.46) after heating the detectors for 4 minutes at 80

◦

C (from [Leroy

and Rancoita (2007)]).

Particle α κ

/κ

theo

[10

−17

A/cm]

1 MeV neutrons 4.56 1.0 1.0

7 MeV protons 17.20 3.8 ± 0.1 0.514

8 MeV protons 13.20 2.9 ± 0.1 0.492

9 MeV protons 13.30 2.9 ± 0.1 0.569

10 MeV protons 9.90 2.2 ± 0.1 0.489

24 GeV/c protons 2.54 0.56 ± 0.01 0.903

is followed by a reverse annealing with an increase of N

eﬀ

(and then of V

) with

time. Heating the detectors at an annealing temperature of 80

◦

C, is accelerating

the room temperature annealing which allows one to reach the intermediate plateau

between the beneﬁcial annealing and the reverse annealing after about 4 minutes of

heating. The change (∆N

eﬀ

) between the value of N

eﬀ

before irradiation (N

eﬀ,0

and the value of N

eﬀ

after irradiation with ﬂuence Φ and after annealing during a

perio d of time t at the temperature T

is given by:

∆N

eﬀ

(Φ, t, T

) = −N

eﬀ,0

+ N

eﬀ

(Φ, t, T

). (6.163)

After heating, N

eﬀ

has to be time scaled by a factor, Θ, given by [Moll (1999)]:

Θ(T

) = exp

−

heat

¶¸

, (6.164)

where E

is the activation energy, k

the Boltzmann constant, T

heat

the tempe-

rature (in K) at which the detector has been heated and T

the temperature (in

K) for which the time has to be scaled. From what is said above, it is understood

that an annealing of 4 minutes at 80

◦

C is applied after each irradiation. After this

annealing, ∆N

eﬀ

is near its minimum, i.e., at the very beginning of the interme-

diate plateau. This heat treatment of 4 minutes at 80

◦

C was performed for all

detectors in [Bechevet, Glaser, Houdayer, Lebel, Leroy, Moll and Roy (2002)] and

corresponds to about 21 days at room temperature (20

◦

C), as found [Moll (1999)]

from Eq. (6.164) with E

= 1.33 eV. Hence, this choice of annealing time and tem-

perature can be viewed as a compromise between i) a temperature high enough to

simulate rather realistically the operation scenario of the LHC, in which irradiation

(running) periods are interspersed with annealing (maintenance shutdowns) periods

and ii) a temperature low enough to excite only the annealing processes occurring

at room temperature.

A comparison done with data obtained for 24 GeV/c proton irradia-

tions [Bechevet, Glaser, Houdayer, Lebel, Leroy, Moll and Roy (2002)] shows that

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534 Principles of Radiation Interaction in Matter and Detection

higher values of the full depletion voltage are necessary to operate beyond the in-

version ﬂuence the detectors irradiated with low-energy protons. As seen before in

Sects. 4.1.3 and 4.2.1 for neutrons

, the concept of radiation hardness factor (κ)

arises from the re-normalization of a particle ﬂuence (Φ) of a particular irradiation

to the 1 MeV neutron ﬂuence equivalent (Φ

= κ Φ. (6.165)

The hardness factor can be extracted from various sources. The NIEL scaling hy-

pothesis provides a theoretical value of the hardness factor. This theoretical value

is given by the ratio of the displacement damage function

(E) for the par-

ticle i and energy E of interest, to the displacement damage function of 1 MeV

neutrons {D

neutron

(1 MeV) = 95 MeV mb, see page 348 and, for instance, [Namen-

son, Wolicki and Messenger (1982); ASTM (1985)]}. Theoretical values for D

(E)

(Sects. 4.2.1.3, 4.2.1.5) can be found for low-energy protons using the Rutherford

scattering formula along with the Lindhard partition function (see page 348) to sep-

arate the displacement damage from the ionization (mathematical expressions avail-

able in [Vasilescu (1997)], tabulated values in [Summers, Burke, Shapiro, Messenger

and Walters (1993)]). The error on the detector thickness (295 ±5 µm) corresponds

to a 3% error on the displacement damage function for 7 MeV protons (energy at

which a maximum variation occurs) [Bechevet, Glaser, Houdayer, Lebel, Leroy, Moll

and Roy (2002)]. Finally, the theoretical hardness factor in a ﬁnite silicon thickness

is found by averaging the damage function over the thickness considered. The theo-

retical hardness factors extracted that way (Table 6.5) will be compared below with

experimental hardness factors extracted from the leakage current of standard planar

silicon detectors exposed to (7–10) MeV protons. The measured value of 0.62 [Rose

Collab. (2001)] is used as the reference hardness factor for 24 GeV/c protons since a

theoretical value cannot be obtained from the method described above for protons

of such momentum. This hardness factor is in agreement with the value of κ ≈ 0.5

estimated from [Huhtinen and Aarnio (1993)]. The value of κ

theo

≈ 0.93 extracted

from [Van Ginneken (1989)] is widely used. However, this value does not ﬁt the

experimental data. The disagreement of experimental data with the values given

in [Van Ginneken (1989)], for energies higher than 100 MeV, is mainly due, among

other physical features, to the assumption in [Van Ginneken (1989)] that all Lind-

hard factors are at their plateau values [Bechevet, Glaser, Houdayer, Lebel, Leroy,

Moll and Roy (2002)].

Hardness factors have been extracted in [Bechevet, Glaser, Houdayer, Lebel,

Leroy, Moll and Roy (2002)] from the leakage current measurements, i.e., from the

evolution of leakage current as a function of the irradiation ﬂuence. The measure-

ments of the detector leakage current were done with the guard ring connected. The

measurements were performed at room temperature (T

) and the leakage current

was re-normalized to T = 20

◦

C using Eq. (6.78). The leakage current per unit

In case of neutron irradiations, the reader can see Eq. (4.79).

One can refer to Sects. 4.2.1–4.2.1.5 for a treatment of the diplacement function.

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Solid State Detectors 535

Table 6.7 Value of the parameters in Eq. (6.167) extracted from the eﬀective doping

concentration (from [Leroy and Rancoita (2007)]) as a function of the proton ﬂuence

(Fig. 6.48). The detectors have been heated 4 minutes at 80

◦

C. The quoted errors are

the errors on the ﬁt. The experimental errors (≈8%) are not included. The parameter

24GeV/c

is the slope for 24 GeV/c protons.

Energy N

eﬀ,0

b c (b/b

24 GeV/c

)

(10

−3

) 10

−2

−1

(10

−14

)

7 MeV 18.4 4.80 ± 0.12 19.3 8.62 ± 0.25

8 MeV 18.4 4.27 ± 0.12 17.2 7.67 ± 0.24

9 MeV 18.6 4.35 ± 0.12 17.0 7.81 ± 0.24

10 MeV 17.7 3.40 ± 0.10 11.3 6.10 ± 0.20

24 GeV/c 17.9 0.56 ± 0.01 2.12 1.00 ± 0.02

volume (I

v ol

) as a function of ﬂuence (Φ) is given by Eq. (6.161). Figure 6.46

shows the results of ﬁtting Eq. (6.161) to the experimental data for low-energy [(7–

10) MeV] protons and high-energy (24 GeV/c) protons after heating for 4 minutes

at 80

◦

C. The values of the α parameter extracted for the various irradiations by

this procedure are shown in Table 6.6.

Studies have shown that the evolution of the leakage current as a function of

ﬂuence and annealing time is independent of the initial resistivity and impurity con-

centration [Moll (1999)]. It is thus possible to obtain the hardness factor (κ

) for

the protons by comparing the values of the α parameter obtained from the proton

irradiations to the value obtained for 1 MeV neutrons (α = 4.56×10

−17

A/cm). The

α parameter was extracted for the volumic leakage current observed in the silicon

detectors heated 4 minutes at 80

◦

C. The values of the hardness factor (κ

) ex-

tracted by this method are reported in Table 6.6. It can be seen in this table that

for low-energy protons, the experimental hardness factors (κ

) are about half the

theoretical hardness factors (κ

theo

) predicted by the NIEL scaling hypothesis (shown

in Table 6.5). The factors (κ

) and (κ

theo

) are in agreement for 24 GeV/c protons,

with the value κ

= 0.56 ± 0.1 in agreement with the referenced experimental va-

lue [Rose Collab. (2001)] of 0.62 and close to the value of ≈ 0.50 estimated from the

displacement damage function. For example, when the hardness factors for 10 MeV

and 24 GeV/c protons are compared, they diﬀer by a factor of 4 if κ

is used and

by about a factor 7 when using κ

theo

Using this hardness factor (κ

), the data have been plotted as a function of the

equivalent ﬂuence [Φ

, Eq. (6.165)] in Fig. 6.47.

Comparison between radiation damage inﬂicted to silicon detectors by low-

energy and high-energy protons can also be extracted from the measurement of the

slope parameter of the eﬀective doping concentration. The standard method ap-

plied to extract the eﬀective doping concentration (N

eﬀ

) of a semiconductor diode

is based on the measurement of the capacitance (C) which is a function of the ap-

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536 Principles of Radiation Interaction in Matter and Detection

Table 6.8 A few examples of proton, neutron and photon re-

actions with silicon (from [Leroy and Rancoita (2007)]). The

probability of these reactions to occur depends on their energy

thresholds.

Energy b b/κ

theo

b/κ

(10

−2

−1

) (10

−2

−1

) (10

−2

−1

)

7 MeV 4.80 ± 0.12 0.649 1.263

8 MeV 4.27 ± 0.12 0.724 1.472

9 MeV 4.35 ± 0.12 0.853 1.500

10 MeV 3.40 ± 0.10 0.756 1.545

24 GeV/c 0.56 ± 0.01 0.903 1.000

plied bias (V ) [Eqs. (6.35, 6.22)]. Hence, a plot of the measured capacitance as a

function of the applied voltage will yield the value of the voltage (V

) necessary to

fully deplete a detector of thickness w [X(V

) = w]:

eﬀ

| =

2 ² V

q w

. (6.166)

The eﬀective doping concentration (N

eﬀ

) as a function of ﬂuence (Φ) can be de-

scribed by Eq. (6.75) rewritten as:

eﬀ

| = | − N

eﬀ,0

exp(−c Φ) + b Φ|, (6.167)

where N

eﬀ,0

is the initial eﬀective doping concentration and c the so-called donor

removal constant assuming a complete removal of the initial eﬀective doping con-

centration after exposure to a high irradiation ﬂuence (Φ À 1/c). The parameter b

describes the introduction of negative space-charge and depends on the annealing

time after irradiation. The value of the parameters extracted by ﬁtting Eq. (6.167)

to the experimental data plotted in Fig. 6.48 are shown in Table 6.7.

It is observed by comparing the values of the slope parameter b of N

eﬀ

(Table 6.7)

that the slopes for low-energy protons are larger than those (b

24GeV/c

) for 24 GeV/c

protons by a factor of 6 to ∼ 9. This reﬂects higher radiation damage inﬂicted

to silicon detectors by low-energy protons compared to 24 GeV/c protons. These

increase factors are close to the ones predicted by the NIEL scaling hyp othesis

(factor of 7 to 12, Table 6.5). However, it is not possible to scale the slope parameter

b by a single hardness parameter: neither by the theoretical factor (κ

theo

), nor by

the experimental factor (κ

) determined from the α value (Table 6.8).

This investigation of irradiation of Standard planar silicon detectors with low-

energy protons demonstrates the limits of applicability of the NIEL scaling hypothe-

sis if used to predict radiation damage produced by diﬀerent particles with diﬀerent

energies. On one hand, it was demonstrated that the absolute values of the hardness

factors determined from the displacement damage function κ

theo

do not agree with

the measured hardness factors κ

. On the other hand, it was shown that individual

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Solid State Detectors 537

-2

-1

1 10 10

7 MeV

8 MeV

9 MeV

10 MeV

24 GeV/c

Proton fluence (10

p cm

-2

)

Effective concentration (10

-3

)

Fig. 6.48 Eﬀective doping concentration (N

eﬀ

in units of 10

−3

) as a function of the proton

ﬂuence (Φ in units of 10

p cm

−2

) after heating for 4 minutes at 80

◦

C (reprinted from Nucl.

Instr. and Meth. in Phys. Res. A 479, Bechevet, D., Glaser, M., Houdayer, A., Lebel, C., Leroy,

C., Moll, M. and Roy, P., Results of irradiation tests on standard planar silicon detectors with

7–10 MeV protons, 487–497, Copyright (2002), with permission from Elsevier).

damage parameters (e.g., leakage current increase and the slope parameter of N

eﬀ

)

have a diﬀerent scaling with the particle energy.

A simulation model of migration and clustering of the produced primary defects

in silicon exposed to various types of hadron irradiation has been developed in

[Huhtinen (2002)]. This model predicts violation of NIEL scaling both for the leakage

current constant (α) and the b-slope of the eﬀective doping concentration after type-

inversion. According to this model the violation is expected in opposite direction

and most pronounced in the case of low-energy protons. These simulation results are

in very good agreement with the data on low-energy protons reported in [Bechevet,

Glaser, Houdayer, Lebel, Leroy, Moll and Roy (2002)], in particular for the 10 MeV

proton data.

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Chapter 7

Displacement Damage and Particle

Interactions in Silicon Devices

The results reviewed in the Chapters on Radiation Environments and Damage in

Silicon Semiconductor and Solid State Detectors and their interpretation show a

progressive understanding of the physics phenomena underlying the displacement

damage eﬀects resulting from the radiation interaction in silicon semiconductors. Al-

though there is no general model supporting a comprehensive interpretation of the

characteristics after irradiation, the generation of complex defects is certainly among

the fundamental mechanisms responsible for the degradation of the silicon prop-

erties. These deep defects are mostly created by non-ionizing energy-loss (NIEL)

processes, which generate primary defects by the initial particle interaction and by

the cascade generation due to silicon recoil, and secondary defects caused by the

diﬀusion of the primary point defects (interstitials and vacancies). The diﬀerent

extension of the cascade and concentrations of impurities favor a slight dependence

of the damage eﬀects on type and energy of the incoming particle, as well as, on

the type and resistivity of the semiconductor. A review of particle interaction and

displacement damage in silicon devices operated in radiation environments was pro-

vided by Leroy and Rancoita (2007).

Radiation-induced defect centers have a major impact on the electrical behavior

of semiconductor devices and deeply aﬀect their properties. For instance, centers

with energy-levels near the mid-gap make signiﬁcant contribution to carrier gener-

ation. Thermal generation of electron–hole pairs dominate over capture processes

when free carrier concentrations are much lower than the thermal equilibrium va-

lues, as in the depletion regions. These centers become the main mechanism for

the increase of the leakage current in silicon devices after irradiation. In general,

radiation-induced defect centers are the relevant mechanism for the decrease of the

minority-carrier lifetime. In addition, donors or acceptors can be compensated by

deep-lying radiation-induced centers resulting in the decrease of the concentration

of majority carriers. This process causes the variation of the device properties de-

pending on the majority-carrier concentration. Measurements of the bulk and p −n

junction properties have shown largely modiﬁed behaviors as function of the tempe-

rature. Furthermore, there are indications that further understanding of transport

mechanisms in irradiated semiconductors is needed by means of additional syste-

539