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

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380 Principles of Radiation Interaction in Matter and Detection

In summary (see Table 4.5), for particle energies of typical space and high-energy

physics environments, the energy deposited by ionization is about 3–4 orders of

magnitude larger than that deposited by damage-energy for charged particles and

isotopes, while they diﬀer marginally for fast neutrons.

4.2.3.2 Ionization Damage

Total ionizing dose (TID) causes the threshold voltage to change due to charge trap-

ping in the SiO

gate insulator. Ionization creates electron-hole pairs in MOS gate

oxide. In semiconductor oxide layers, such as SiO

, electrons produced by ionization

rapidly move from the oxide layer, under the inﬂuence of the electric ﬁeld created by

the bias voltage. The holes, having lower mobility, diﬀuse slowly near the Si–SiO

interface, where they will accumulate as a charged layer, modifying the operating

features of the device. The presence of these trapped holes is responsible for an elec-

trical ﬁeld which induces a negative shift of the threshold voltage, modifying the

operating features of the device (NMOS and PMOS transistors). This eﬀect is re-

duced by the recombination of some of the electrons with holes so reducing, in turn,

the amount of holes trapped in the oxide and, consequently, reducing the negative

shift of the threshold voltage. This shift is dose-rate dependent as a high dose-rate

induces a high instantaneous density of electron-hole pairs, i.e., part of the electrons

cannot leave far the oxide and recombine very fast, causing enhancement of the re-

combination rate and reduction of the shift. In case of low dose-rate, the induced

low instantaneous density of electron-hole pairs allows electrons to quickly leave the

oxide reducing the recombination eﬀect and the shift. After some time, a fraction

of the holes will leave the oxide at the Si–SiO

interface and generate defects in Si

near the interface reducing the carriers mobility. These defects are traps for electrical

charges depending on the bias applied on the gate. In PMOS transistors, the nega-

tive bias applied on the gate and the positive charges trapped in the interface states

- trapped holes in gate oxide - produce an electrical ﬁeld which induces a negative

shift of the threshold voltage which enhances the threshold voltage shift initially

produced by the gate oxide trapped holes. In NMOS transistors, the positive bias

applied on the gate and the negative charges trapped at the interface produce an

electrical ﬁeld which induces a positive shift of the threshold voltage which depletes

the threshold voltage shift initially produced by the gate oxide trapped holes. This

eﬀect in NMOS transistors is also rate dependent since it depends on the density of

interface states which depends, in turn, on the holes density accumulated in the gate

oxide near the Si–SiO

interface. In PMOS transistors, the global threshold-voltage

shift is always negative and increases with decreasing dose-rate, while in NMOS

transistors the global threshold-voltage shift depends on the ratio between oxide

charge density and interface charge density which both increase with decreasing

dose-rate. In MOS transistors, TID eﬀects also result in varying the sub-threshold

slope (e.g., see Chapter 1 in [Ma and Dressendorfer (1989)], also [Codegoni et al.

(2004a)] and references therein). In irradiated bipolar transistors the density of

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Radiation Environments and Damage in Silicon Semiconductors 381

energy states, at the interface between silicon and oxide surrounding the emitter,

is high and induces a parasitic base-current from the recombination of minority

carriers (injected from the emitter into the base) with majority carriers (from the

base). The parasitic current, added to the regular base current decreases the gain of

the bipolar transistor. However, at high collector current, saturation of the interface

states by carriers from the emitter and recombination with majority carriers from

the base brings the parasitic base current to a saturation value, which becomes

negligible and therefore the gain is almost unchanged from its value before irradia-

tion. At low collector current, the absence of interface states saturation maintains

the parasitic recombination current and degrades the gain compared with its value

before irradiation. Again, TID (see page 293) induces higher interface state density

at low dose-rate compared with high dose-rate and gain degradation induced by

TID is higher at low dose-rate than at high dose-rate. The degradation of bipolar

transistor performance by TID that increases when dose-rate decreases is called

low dose-rate eﬀect (LDRE) and becomes signiﬁcant with dose-rate ∼ 50 rad s

−1

and increases continuously with dose-rate decreasing down to 1 × 10

−3

rad s

−1

even less. LDRE also occurs for low TID (a few krads). From the above discussion,

LDRE depends on the device architecture, the structure and thickness of the oxide

layer surrounding the emitter and on bias conditions. LDRE degrades performance

of the bipolar circuits, in particular by degrading the gain of ampliﬁers, of input

oﬀset voltages and input bias currents.

The ionizing dose aﬀects other devices, for instance the ﬁeld eﬀect transistors. A

treatment of TID eﬀects is beyond the purpose of the present book. However

a detailed discussion of these eﬀects can be found in literature (e.g., see [Ma

and Dressendorfer (1989)], Chapter 6 of [Messenger and Ash (1992)], Chapter 6

of [Claeys and Simoen (2002)], [Holmes-Siedle and Adams (2002)] and, also, the

chapter on Displacement Damage and Particle Interactions in Silicon Devices and

references therein). A survey of radiation damage in semiconductor devices is given

in [ECSS (2005)].

4.3 Radiation Induced Defects and Modiﬁcation of Silicon Bulk

and p − n Junction Properties

Defects and clusters of defects do not behave as donors or acceptors which are

intentionally introduced into lattice sites to modify in a controlled-way the intrinsic

properties of a semiconductor

∗

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

of semiconductor devices and can deeply aﬀect their properties (e.g., see [Srour,

Long, Millward, Fitzwilson and Chadsey (1984); Srour and McGarrity (1988)] and

∗

Studies have been carried out to investigate the improvement of the radiation hardness by the

so-called defect-engineering (see for instance [Kozlovski and Abrosimova (2005); Msimanga and

McPherson (2006)] and references therein).

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382 Principles of Radiation Interaction in Matter and Detection

references therein). For instance, centers with energy-levels near the mid-gap make

a signiﬁcant contribution to carrier generation. Thermal generation of electron–

hole pairs dominates over capture processes, when the free carrier concentrations

are much lower than the thermal equilibrium values, like in the depletion re-

gions (e.g., see Chapter 6 in [Grove (1967)]). These centers become the main me-

chanism for increasing the leakage current in silicon devices after irradiation. Fur-

thermore, the electron-hole recombination occurs when a free carrier of one sign can

be captured at defect centers (or recombination centers), followed by capture of a

carrier of the opposite sign. Radiation-induced recombination centers is the relevant

mechanism to decrease the minority-carrier lifetime which, in turn, is the dominant

mechanism for gain degradation in bipolar transistors (e.g., see Sect. 7.1). In ad-

dition, donors or acceptors can be compensated by deep-lying radiation-induced

centers. That results in the decrease of the concentration of majority carriers. This

process (referred to as carrier removal) causes the variation of the device properties

depending on majority carrier concentration, for example the increase of collector

resistance in bipolar transistors. Temporary trapping of carriers can typically occur

at a shallow level, with no recombination. Both majority- and minority-carriers can

be trapped (in separate levels). Moreover, a tunneling process can allow the passage

through a potential barrier by means of defect levels. For example, there may be a

defect-assisted tunneling component of the reverse current in p −n junction diodes.

4.3.1 Displacement Damage Eﬀect on Minority Carrier Lifetime

Among the most important semiconductor material-parameters for practical appli-

cations in electronic devices, we have the (excess-) carrier lifetime, the equilibrium

majority-carrier concentration and the majority-carrier mobility (e.g. see [Schroder

(1997)]). To a ﬁrst approximation

†

, the rate at which the electrical properties of

semiconductors are degraded by irradiation is often expressed in terms of a damage

coeﬃcient. For instance, the minority carrier (recombination) lifetime, τ , is given

irr

−

≡ ∆

τ,i

, (4.125)

where τ

irr

and τ are the lifetimes after and b efore the irradiation with a ﬂuence Φ

of particles, respectively; K

τ,i

is the (recombination) lifetime damage coeﬃcient

‡

which may depend on a) the type of substrate, b) the dopant concentration, c)

the level of compensation and d) the type (“i”) and energy of irradiating particles

†

The linear dependence on the particle ﬂuence [see Eq. (4.125)] is expected as long as the steady-

state Fermi level is not signiﬁcantly moved.

‡

A coeﬃcient that is the reciprocal of that given in Eq. (4.125) is also found and used in literature

(e.g., see Section 7.2.1 of [van Lint, Flanahan, Leadon, Naber and Rogers (1980)] and references

therein).

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Radiation Environments and Damage in Silicon Semiconductors 383

(e.g., see Section 5 in Chapter I of Part II of [Vavilov and Ukhin (1977)], Section 3.4

of [Srour, Long, Millward, Fitzwilson and Chadsey (1984)], [Srour and McGarrity

(1988)] and references therein). The values of K

τ,i

can be usually found in liter-

ature. For instance for low-resistivity silicon, experimental results on the lifetime

damage constants are presented in [Srour, Othmer and Chiu (1975)] for 0.5, 1.0 and

2.5 MeV electrons with ﬂuences up to ' 3 × 10

e/cm

and 10 MeV protons with

ﬂuences up to ' 1.2 × 10

p/cm

(see also Section 3.4 of [Srour, Long, Millward,

Fitzwilson and Chadsey (1984)]). Furthermore, the damage constant K

τ,n

was ex-

tensively investigated

††

for fast-neutron ﬂuences (typically) up to 10

–10

n/cm

and its values

are available in literature. For n- and p-type silicon, K

τ,n

is almost

independent of the silicon resistivity (below a few Ω cm). In addition, the anneal-

ing eﬀect on the carrier lifetime was studied at room temp erature: the minority-

carrier lifetime was found to undergo both short-term and long-term annealing (see

pages 32–45 in [Srour, Long, Millward, Fitzwilson and Chadsey (1984)] and [Srour

(1973)]).

For a fast-neutron irradiation with a spectral ﬂuence φ(E) [where E is the kinetic

energy of the neutron, see Eq. (4.77)], the ratio Φ

τ,n

can be re-expressed to

account for the creation of recombination centers and the absorption of minority

carriers as {see Equation (5.15) of [Messenger and Ash (1992)], and also [Codegoni et

al. (2004b); Consolandi, D’Angelo, Fallica, Mangoni, Modica, Pensotti and Rancoita

(2006)]}:

τ,n

= σ

min

c,n

(E) φ(E) dE

= σ

<σ

c,n

> Φ

, (4.126)

where n

is the number of atoms per cm

in the bulk silicon [Eq. (4.82)], E

min

is the minimal threshold of the neutron energy for inducing displacement damage

(see page 348), Φ

is the fast-neutron ﬂuence [Eq. (4.78)], v

is the average speed

of minority carriers, σ

is the cross section for the absorption of minority carriers

by recombination centers; σ

c,n

(E) and < σ

c,n

> are the cross section of neutrons

with energy E for creation of recombination centers in silicon and its average value,

respectively. <σ

c,n

> is computed according to

<σ

c,n

min

c,n

(E) φ(E) dE

. (4.127)

The term

= n

min

c,n

(E) φ(E) dE

= n

<σ

c,n

> Φ

[cm

−3

] (4.128)

††

The reader can see, e.g., [Messenger (1967b); Srour (1973)], Section 5 in Chapter I of Part II

of [Vavilov and Ukhin (1977)], Section 5.9 of [Messenger and Ash (1992)] and references therein.

Below 2–3 Ω cm [Messenger (1967b)], for n-type silicon K

τ,n

is ' (1.0–1.6) × 10

s/cm

and for

p-type silicon K

τ,n

' (1.5–3.0) × 10

s/cm

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384 Principles of Radiation Interaction in Matter and Detection

is the concentration of recombination centers resulting from the displacement pro-

cesses induced by the fast-neutrons. To a ﬁrst approximation (e.g., see Sects. 7.1.1

and 7.1.3), in absence of saturation eﬀects

, (mostly) for low-resistivity silicon we

can assume that the concentration of recombination centers is proportional to the

energy deposited by non-ionizing energy-loss (NIEL) processes per unit volume E

dis

(Sect. 4.2.1) and, consequently [see Eq. (4.83)], to the concentration of Frenkel-pairs

(FP ) introduced as primary point-defects. For instance, in low-resistivity silicon the

concentration of dopants is suﬃciently large to keep them participating to the phe-

nomenon of complex-defect formation even at large neutron ﬂuences, although this

process reduces the concentration of available impurities. Therefore, Eq. (4.128) can

be expressed as

dis

∝ C

= γ

dis

FP. (4.129)

For deep defects resulting from primary defects mostly created by cascading-

displacement processes, the term γ

dis

may result to be slightly

(if at all) dependent

on the type of incoming particles.

By means of Eqs. (4.128, 4.129), Eq. (4.126) can be rewritten as

τ,n

= σ

dis

FP , (4.130)

where σ

and ν

are almost independent of the properties of the fast-neutron spec-

tral ﬂuence. These latter terms, similarly to the parameter γ

dis

, are expected to

be slightly (if at all) dependent on the type of the incoming particle, when deep

defects result from primary defects mostly created by cascading-displacement pro-

cesses. Furthermore, by combining Eqs. (4.125, 4.130), (mostly) for low-resistivity

silicon we obtain

irr

−

τ,i

' λ FP, (4.131)

where

λ = σ

dis

is almost independent of the type and energy of the incoming particle, but depends

on i) the type of substrate, ii) (slightly) the dopant concentration and iii) the level of

compensation. Equations (4.129, 4.131) indicate that an approximate NIEL scaling

(e.g., see Sect. 4.1.1.2) is expected for the variation of the reciprocal of the minority-

carrier lifetime in low-resistivity silicon.

Finally, it has to be added that expressions similar to Eq. (4.125) have been

formulated for the generation lifetime (e.g., see Section 11.2.4 of [Lutz (2001)]),

For high-resistivity silicon (see discussion in Sect. 4.3.5), it was found that there are secondary

defects whose concentrations are not linearly dependent on ﬂuence.

NIEL scaling violation was observed in high-resistivity silicon (e.g., see Sect. 6.8.3).

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Radiation Environments and Damage in Silicon Semiconductors 385

minority-carrier diﬀusion length (e.g., see Section 3.2.7.2 of [Holmes-Siedle and

Adams (2002)]), majority-carrier mobility and concentration (e.g., see Section 7.2.2

of [van Lint, Flanahan, Leadon, Naber and Rogers (1980)]).

4.3.2 Carrier Generation and Leakage Current

Silicon detectors are usually one-sided

∗∗

− n junctions

‡

and are referred to as

n-type silicon detectors. In these detectors, the highly doped p

-region (usually with

a dopant concentration of ≈ 10

−3

) extends over ≈ 0.5 µm at a depth of (2–

2.5) µm and is on top of a lowly doped n-substrate (with a dopant concentration of

≈ 6× 10

–2.4×10

−3

), whereas on the rear-side there is a highly doped n

-layer

of ≈ 0.5 µm thickness also at a depth of 2–2.5 µm and with a dopant concentration

of ≈ 10

−3

(sometimes indicated as n

). One of the purposes of the n

-region

is to allow the n-substrate to make a good external ohmic-connection

††

(e.g., see

Section 5.1 of [Sze (1985)] and Appendix B9 of [Ng (2002)]) with, for instance, the

external bias supplier. In these devices, the electrical characteristics (for example,

I − V and C − V ) are determined by those of the one-sided p

− n junctions.

At room temperature, when a reverse voltage

‡‡

, V

, smaller than the breakdown

voltage and larger than (3k

T )/e ≈ 78 mV

∗

is applied to a non-irradiated silicon de-

tector, the reverse current density

†

is approximated by the sum of both the diﬀusion

density current in the diﬀusion regions and the generation current in the depletion

region (see, for instance, [Sah, Noyce and Shockley (1957); Moll (1958)], Section 3.4

of [Sze (1985)], Sections 3.7–3.8 of [Messenger and Ash (1992)], Sections 9.1–9.4

of [Bar-Lev (1993)] and Chapter 8 of [Neamen (2002)]):

≈ J

e n

int

, (4.132)

where τ

is the eﬀective generation lifetime, n

int

is the intrinsic carrier concentra-

tion (e.g., see Chapter 6), W is the depletion layer width and J

is the so-called sa-

turation current density. It can be shown that only those generation-recombination

centers with an energy level near the intrinsic Fermi level can signiﬁcantly con-

tribute to the generation rate (see for instance [Sah, Noyce and Shockley (1957)]

∗∗

The one-sided p

−n junctions [Wolf (1971)] are asymmetrical step-junctions in which the p-side

is much more heavily doped than the adjacent n-side.

‡

For a description of the properties of the p − n junctions, one can see, for instance, Section 6.2

of [Wolf (1971)].

††

The non-rectifying metal-(n

-)semiconductor contact results in an almost abrupt junction with

the built-in potential determined by the metal work-function, the electron aﬃnity of the semicon-

ductor and the potential diﬀerence between the Fermi level and the bottom level of the conduction

band; the current transport is mainly due to majority carriers (e.g., see pages 160–171 of [Sze

(1985)]).

‡‡

In this Section, V

indicates the absolute value of the reverse voltage.

∗

is the Boltzmann constant, T the is temperature in Kelvin and e = 1.6 × 10

−19

C is the

electronic charge.

†

The contribution of the surface leakage current (e.g., see Section 10.3 of [Grove (1967)]) has not

been taken into account in Eq. (4.132) (see also Sects. 6.1.6).

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386 Principles of Radiation Interaction in Matter and Detection

and Section 3.4 of [Sze (1985)]). For an n-type silicon detector, the saturation den-

sity current is expressed by that of the real diode equation, i.e.:

≈ e

int

, (4.133)

where N

is the donor concentration, D

and τ

are the diﬀusion coeﬃcient and the

lifetime of holes in the n-region, respectively.

As mentioned above, radiation-induced defect centers, whose energy levels are

near the intrinsic Fermi level, can become a relevant source for carrier generation

and determine the increase of the volume-generated reverse-bias current inside the

depleted region of silicon devices. Since, to a ﬁrst approximation, the concentration

of defects is proportional to the particle ﬂuence, the reverse current after the irradi-

ation (I

r,irr

) is expected to increase with increasing particle ﬂuence. Experimental

studies

∗

carried out on reverse-biased silicon detectors have conﬁrmed that I

r,irr

(in A) depends, to a ﬁrst approximation, linearly on the particle ﬂuence:

r,irr

' I

+ α

vol

, (4.134)

where I

(in A) is the detector leakage current before the irradiation at a ﬂuence

(in particles/cm

), V

vol

(in cm

) is the depleted volume of the detector and α

(in A/cm) is the so-called radiation-induced reverse current damage constant. This

latter coeﬃcient depends, in turn, on the type (“i”) and energy of the irradiating

particles (see Sects. 4.2.1.1–4.2.1.5). The processes resulting in self-annealing at

room temperature (see page 373) allow the leakage current to decrease with time.

The time dependence of the leakage current was investigated from 1.5 hours up

to 26 months after the irradiations of high-resistivity

†

Fz silicon detectors exposed

to 2 MeV neutrons with ﬂuences between 4.8 ×10

and 1.3 ×10

n/cm

[SICAPO

Collab. (1994b)]. The detectors were stored and kept at room temperature. The mea-

surements were performed at a temperature of 20

◦

C and at full depletion voltage. It

has been determined that the reverse current damage constant (α

) decreases with

time as

= 10

−b

× 10

−17

[A/cm], (4.135)

where a = 1.17 ±0.01, b = (1.45 ±0.86) ×10

−1

and t (≥ 1.5) is the numb er of hours

after the irradiation [SICAPO Collab. (1994b)]. After a long-term annealing, the

reverse current damage constants are ≈ 2 × 10

−17

[A/cm] and ≈ 3 × 10

−17

[A/cm]

for 1 MeV neutrons and minimum ionizing protons (and pions), respectively (see

Section 28.8 of [PDB (2008)] and, also, [Moscatelli et al. (2002)]).

At higher fast-neutron ﬂuences, a stronger rise of I

r,irr

as function of the neu-

tron ﬂuence was observed (see, for instance, Fig. 11.11 in Section 11.2.4 of [Lutz

∗

One can see, for instance, Sect. 6.8.2 and, also, [Fretwurst et al. (1993); Leroy, Glaser, Heijne,

Jarron, Lemeilleur, Rioux, Soave and Trigger (1993); SICAPO Collab. (1994b)], [Bechevet, Glaser,

Houdayer, Lebel, Leroy, Moll and Roy (2002)], Section 6.4.1 of [Holmes-Siedle and Adams (2002)]

and references therein.

†

The resistivities were between (4–7) kΩ cm.

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Radiation Environments and Damage in Silicon Semiconductors 387

(2001)]). In fact, at these ﬂuences, the I − V reverse characteristics are largely

modiﬁed (e.g., see Sect. 4.3.3.1) and determine an increase of the eﬀective reverse

current damage constant.

4.3.3 Diode Structure and Rectiﬁcation Down to Cryogenic

Temperature

The characteristics of semiconductor diodes, like those of other semiconductor de-

vices, are substantially aﬀected by irradiation. The rate and level of radiation

changes involve the properties of the bulk region, of the ohmic contact and the

surface eﬀects. Thus, at large ﬂuences, both the forward and reverse I − V cha-

racteristics are diﬀerent with respect to those of a non-irradiated diode. After ir-

radiation, these characteristics depend on the type and ﬂuence of particles and on

the junction and bulk properties of the silicon. For instance, at large particle ﬂu-

ences, semiconductor diodes lose (largely) the features of being a rectifying device

to become more similar to linear semiconductor resistors with a low (germanium) or

high (silicon) resistivity (see for instance Section 1 in Chapter II of Part I I of [Vav-

ilov and Ukhin (1977)], [Croitoru, Gambirasio, Rancoita and Seidman (1996)] and

references therein).

4.3.3.1 Rectiﬁcation Property Up to Large Fast-Neutron Fluences at Room

Temperature

The rectiﬁcation property of a p − n diode results from the creation of a depletion

region at thermal equilibrium. It is one of the most important characteristics of

non-irradiated p − n junctions, that is they allow current to ﬂow easily in one

direction. When we apply a forward bias, the electrostatic potential across the

junction region is reduced from that of the thermal equilibrium [the so-called built-in

potential, see Eq. (6.12)], thus the diﬀusion of majority carriers from one to the other

side of the junction is enhanced and, as a consequence, the forward current increases

rapidly with increasing voltage. However, under reverse bias, the applied voltage

increases the electrostatic potential across the depleted region, as a consequence

determines a decrease of the diﬀusion currents and, ﬁnally, results in a small reverse

(or leakage) current. As the reverse bias is increased, the reverse current remains

very small [Eq. (4.132)], until a critical voltage (the so-called breakdown voltage) is

reached. Above the breakdown voltage, the reverse current becomes very large

‡

The forward current-voltage characteristics of a non-irradiated diode accounts

for both the diﬀusion and recombination currents (see for instance [Sah, Noyce

and Shockley (1957); Moll (1958)], Section 3.4 of [Sze (1985)], Sections 3.7–3.8

of [Messenger and Ash (1992)], Sections 9.1–9.4 of [Bar-Lev (1993)] and Chapter 8

of [Neamen (2002)]). In fact under low-injection condition

and assuming that the

‡

This phenomenon is also referred to as junction breakdown.

This condition is satisﬁed when the injected minority carrier concentrations are small compared

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388 Principles of Radiation Interaction in Matter and Detection

depletion region of the diode has abrupt boundaries, the ideal diode equation for

the density current due to carrier diﬀusion (J

f,diﬀ

) is replaced by the real diode

equation:

' J

f,diﬀ

e n

int

2τ

exp

e V

2 k

, (4.136)

where V

is the applied forward voltage

, τ

is the eﬀective recombination lifetime,

int

is the intrinsic carrier concentration, W is the depletion layer width and J

f,diﬀ

is given by

f,diﬀ

= J

exp

e V

− 1

. (4.137)

is the saturation current density and is given by Eq. (4.133) for n-type silicon

detectors. The second term of Eq. (4.136) accounts for the so-called generation

current in the depletion layer width. It can be shown that only those generation-

recombination centers with an energy level near the intrinsic Fermi level can con-

tribute signiﬁcantly to the recombination rate (see for instance [Sah, Noyce and

Shockley (1957)] and Section 3.4 of [Sze (1985)]).

In general, the measured forward currents can be represented empirically by:

∝ exp

e V

η k

, (4.138)

where η is referred to as ideality factor

. At ro om temperature, in silicon p − n

diodes the recombination current dominates at low-forward voltages, while for V

0.5 V the diﬀusion current dominates (e.g., see Fig. 6.24 in Section 6.6.b of [Grove

(1967)]). At even larger forward currents, the ideality factor becomes again larger

than 1. This phenomenon results from the eﬀect of series resistance and from the

high-injection of carriers.

In p − i − n diodes, there is an almost-intrinsic (or a weakly doped) layer sand-

wiched between the heavily doped p

- and n

-regions

∗∗

. In practice, the central

region is either weakly doped p-type (indicated as π-) or weakly doped n-type (in-

dicated as ν-) silicon, with typical dopant concentrations of ≈ (10

–10

) cm

−3

and ranges ≈ (10–200) µm (see, for instance, Chapter 2 of [Ng (2002)]). In these

diodes, the I −V characteristic is approximately expressed by (e.g., see Section 15.2d

of [van der Ziel (1976)], Sections 3.1–3.3.1.1 of [Ghandhi (1977)], Section 11.2

of [Tyagi (1991)], Chapter 2 of [Ng (2002)], see also [Fletcher (1957); Nussbaum

(1973)]):

f,pin

∝ F

exp

e V

m k

, (4.139)

with the majority carrier concentrations.

In this Section V

indicates the absolute value of the applied forward voltage.

The ideality factor is ' 1 when the diﬀusion current dominates, ' 2 when the recombination

current dominates.

∗∗

The size of the n

-region (see for instance the doping proﬁles of a silicon p

− n − n

power

rectiﬁer in Section 18.1.1 of [Tyagi (1991)] and references therein) is such that it does not operate

only as an ohmic contact, as it occurs in p

− n junction.

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 389

Fig. 4.25 Reverse (R

) and forward (R

) resistances in kΩ as functions of the fast neutron ﬂuence

in n/cm

at room temperature (from [Leroy and Rancoita (2007)]; see also [Croitoru, Gambirasio,

Rancoita and Seidman (1996)]). The dotted and dashed lines are to guide the eye. For these

detectors the equivalent resistance, in case of an intrinsic silicon medium, was calculated for an

intrinsic silicon resistivity of about 2.3 × 10

Ω cm at 300 K (see, for instance, Table 1.20 of [Wolf

(1971)]).

where 1 < m < 2 depends on the dopant concentrations and on the levels of

the recombination centers [Nussbaum (1973)]. F

is a function of the ratio w/L

where w is the thickness of the quasi-intrinsic layer and L

is the ambipolar diﬀusion

length: it reaches its maximum value (≈ 0.3) for w/L

≈ 1 (e.g., see Sections 3.1–

3.3.1 of [Ghandhi (1977)]).

At room temperature, the forward (and reverse) I − V characteristics of n-

type silicon detectors

††

of 400 µm thickness and resistivity (4–6) kΩ cm have been

measured before and after irradiation with fast-neutrons. Before irradiation, for

3.8 .

e V

. 25

these low-doped devices exhibit an ideality factor which is larger than that expected

from Eq. (4.138) and becomes ≈ 4 at large V

[SICAPO Collab. (1995d)]

∗

. After

††

The dopant concentrations of the layers are close to those indicated at page 385.

∗

The ideality factor was also found to be larger than expected in 300 µm thick devices [Beattie,

Chilingarov and Sloan (1998)].