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

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570 Principles of Radiation Interaction in Matter and Detection

Fig. 7.10 Example of indirect ionization (from [Leroy and Rancoita (2007)]; see also [Petersen

(1981)]). The 30 MeV proton incident at an angle θ interacts with silicon producing p, α and a

recoiling Mg-ion [the reaction is

Si(p,pα)

Mg with an energy threshold of 10.34 MeV].

electron-hole pairs generated outside the nominal depleted region which would

otherwise recombine or slowly diﬀuse into the depletion region. These charges

from funneling add to the prompt charge and contribute to the prompt compo-

nent of the current pulse. The prompt component consisting of charges collected

by electrical drift in the depletion region and through funneling corresponds to

a collection time from 100 to ∼ 500 ps depending on the time constant of the

charge collection process (Fig. 7.9).

(3) Outside the inﬂuence of any electric ﬁeld, the charges are transported by dif-

fusion, some may even recombine (Fig. 7.8), after a range of several microns

around the impact point of the incoming particle. These charges separated by

a diﬀusion process takes much longer time to be collected or have to traverse

a larger distance through the silicon. They produce a gradual fall time, de-

layed component, following the prompt component. The delayed component is

consisting of charges collected by diﬀusion with a collection time of ∼ 600 ps

to 1 µs or longer [Dodd, Sexton and Winokur (1994)]. The times associated to

the prompt component are in principle short (ps) compared to the devices re-

sponse times (ns). Therefore, the introduction of sub-micron technologies with

response sp eed allowing the propagation, through the circuit, of short signals

(∼ 100 ps) produced by SEE requires the development of adequate techniques

to distinguish SEE occurrences from normal circuit signals.

One can represent the shap e of the pulse, I(t), as a function of time using a

parameter T , which is the time constant for the charge collection process and is the

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Displacement Damage and Particle Interactions in Silicon Devices 571

property of the CMOS process used for the device [Shivakumar, Kistler, Keckler,

Burger and Alvisi (2002)]:

I(t) ≈

× exp

−

, (7.32)

where Q is the amount of charge collected due to a particle strike. It takes more time

for the charge to recombine, if T is large. If T is small, the charge recombines rapidly

and the current pulse is of short duration. T decreases as feature size decreases. A

method of scaling T , based on feature size, can be found in [Hazucha and Svensson

(2000)].

This local current can change the logical state of a cell (SEU). This may occur

in digital, analog and optical components. It may also cause loss of device function-

ality (Latch up) or cause device destruction due to a high current state in a power

transistor (SEB). It may also induce rupture of oxyde gate (SEGR).

7.2.7.2 Indirect Ionization

Direct ionization by high energy protons and neutrons from cosmic rays or produced

by the collisions of particles in particle accelerators or the interaction of cosmic rays

with atmospheric particles do not create enough charge to cause SEE. In circuits

materials (Si, SiO

, GaAs) a proton, for instance, compared to an α-particle has a

stopping power smaller by an order of magnitude and a range larger by an order

of magnitude (see Table 7.1). A proton of 30 MeV of the example [Petersen (1981)]

in Fig. 7.10 will deposit in the maximum path-length available of 30 µm of silicon

(the sensitive volume has a transversal size of 20 µm ×20 µm size and a depth of

10 µm) a direct ionization energy of 0.1 MeV, while the maximum energy deposited

by elastic recoils [see Eq. (4.103)] is

= 4

+ M

)

≈ 4 MeV

(with a Si range, in silicon, of ≈ 2.66 µm) and the maximum energy deposited

by evaporated α-particle emission is 5.3 MeV (with a range, in silicon, of ≈

26.5 µm). The energy deposited by

Mg and the evaporated proton are 0.76 MeV

(with a range, in silicon, of ≈ 1.22 µm) and 0.32 MeV (with a range, in silicon,

of ≈ 3.28 µm), respectively. Then, neutrons and protons can produce upsets by

indirect ionization through their interactions with atoms in the semiconductor (si-

licon) producing α-particles and nuclei if their energy is above a given threshold

(Fig. 7.10).

As they are much heavier than the original proton or neutron, these α-

particles and recoil nuclei can also generate tracks of electron-hole pairs along their

paths. These α-particles and recoil nuclei may induce SEE, if they have enough

energy, and travel in the right direction after their production to deposit enough

charge into the sensitive volume of the circuit. It should be noted that high-energy

α-particles produced by these nuclear reactions may have a range large enough to

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572 Principles of Radiation Interaction in Matter and Detection

escape from the silicon creating less damage or no damage at all, if emitted very

close to the surface of the circuit. The recoiling nuclei deposit energy in the same

way as the directly ionizing heavy-ions, but have a very short range. A variety of

neutron, proton and gamma reactions with silicon can take place with emission of

recoil nuclei, protons, α-particles and γ (Table 7.2). The probability of these re-

actions is depending on their energy threshold as compared to the energy of the

incoming particle. Spallation reactions may also occur, in which the silicon nucleus

is broken into oxygen and carbon fragments (p+Si →p+

C+

O).

Thermal neutrons were shown [Normand (1998)] causing SEE, possibly through

the α-particle (1.47 MeV) and lithium (0.84 MeV) nucleus emission after the cap-

ture reaction

B(n,α)

Li; boron being present as dopant in semiconductor and

passivation layer [Griﬃn (1997)]. In principle fast neutrons interact with Si-atoms

producing relevant recoil energy already at neutron energy around 100 keV, but only

neutrons with an incident energy higher than 3 MeV should contribute to SEU cross

section [Normand (1998)]. It has been observed [Johansson et al. (1998)] that the

measured SEU cross section for SRAM exposed to quasi-monoenergetic neutrons of

ﬁve diﬀerent energies, from 22 to 160 MeV, has an energy threshold and is slowly

increasing with energy up to a saturation value at ab out 100 MeV neutrons energy

(see Sect. 7.2.8 for a discussion of the cross section shape). The energy dependence

of the SEU cross section looks very similar for the variety of SRAM devices tested.

7.2.7.3 Linear Energy Transfer (LET)

The capability of an ion (Z ≥ 2) to interact with a material is a function of its

linear energy transfer (LET) value. LET is the energy deposited per unit length

(dE/dx) along the ion trajectory in the material. The LET is directly proportional

to the square of the atomic number of the incident ion and inversely proportional

to its energy. The amount of energy deposited (and charge created) in a region of a

circuit is proportional to LET as a function of path-length in this region. The LET

used in SEU studies is actually the mass stopping power, i.e.,

LET(x) =

(7.33)

with ρ being the material density. Then, the LET unit is MeV cm

−1

that be-

comes the energy loss per density thickness (t

= ρ x, where x is the absorber

thickness), so that, LET may be quoted roughly independently of the target mate-

rial of the device. The concept of LET does not apply to striking neutron or proton

since SEE in that case are the results of nucleon–nuclear interactions (indirect ioni-

zation) and therefore the path-length distribution through the sensitive volume is

unknown. Then, one refers to the energy of the incident neutron or proton.

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Displacement Damage and Particle Interactions in Silicon Devices 573

Table 7.2 A few examples of proton, neutron and photon reactions

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

these reactions to occur depends on their energy thresholds.

Reaction Energy threshold Comment

(MeV)

Si → n+

Si 0.00 elastic scattering

Si → p+

Al 4.00

Si → α+

Mg 2.75

Si → α+α+

Ne 12.99

Si → p+p+

Mg 13.90

Si → p+α+

Na 15.25

Si → n+

C+

O 16.70

Si → p+

Si 0.00 elastic scattering

Si → α+

Al 7.99

Si → p+α+

Mg 10.34 see Fig. 7.10

Si → p+p+

Al 12.00

Si → p+

C+

O 16.70

Si → α+α+

Na 17.48

Si → n+p+

Si 17.80

γ+

Si → n+

Al 16.97

γ+

Si → n+p+

Al 24.60

γ+

Si → n+n+

Si 30.50

γ+

Si → α+

Mg 17.10

7.2.7.4 Sensitive Volume

The sensitive volume, often called sensitive node in literature, is often approximated

by a rectangular parallelipipeded (RPP approximation) with dimensions length x,

width y, and depth d (Fig. 7.11).

As will be seen later (Sect. 7.2.8), the product x × y (size) can be determined

from the saturation SEE cross section. The thickness or depth, d, is often assumed to

be of the order of a few microns. Measurement of the SEE sensitivity with the angle

of incidence, θ, may help to better deﬁne the value of d. This RPP approximation

has to be often modiﬁed to take into account more complex geometries. However,

the RPP approximation is easy for fast calculation. More complex geometries can

be treated in simulations using co des such as GEANT4 [Agostinelli et al. (2003)].

7.2.7.5 Critical Charge

The RPP model of sensitive volume is assumed in order to estimate the amount

of charge to be released by a charged particle striking a logic circuit and that will

induce a voltage variation changing the memory logic status (bit ﬂip). One may

consider the sensitive volume of the semiconductor-based device, as a parallel plate

capacitor (capacitance C), of size x×y and thickness d; ² is the electric permittivity

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574 Principles of Radiation Interaction in Matter and Detection

Fig. 7.11 The geometry of the RPP approximation. Usually, the thickness d is a few microns

(from [Leroy and Rancoita (2007)]). The incoming particle strikes at an incident angle θ.

of the semiconductor material between the two capacitor plates

C = ² ×

= ² ×

x × y

. (7.34)

In the case of ions (Z ≥ 2) the critical charge corresponds to a linear transfer thresh-

old (LET

). LET

is deﬁned as the minimum LET needed to cause a single event

eﬀect at a particle ﬂuence of 10

ions cm

−2

(according to NASA standards

). Then,

SEE immunity for a device is deﬁned as LET

> 100 MeV cm

−1

[LaBel (1993)].

If a charge Q deposited by a ionizing particle is large enough to induce a voltage

change ∆V , a SEU occurs when Q > Q

. The threshold value of LET, LET

needed to produce the voltage change is

LET

≈ ∆V =

. (7.35)

Using Equation (7.34), we obtain

Q = ∆V × ² ×

x × y

. (7.36)

If ∆V = 1.5 V is the voltage change necessary to ﬂip bit 1 into bit 0 (or vice versa),

one has a critical charge of

= 1.58 × 10

−16

µm

x × y

µm

(7.37)

with a device thickness d = 1 µm (for silicon, ² = 1.05 × 10

−16

F µm

−1

). From

Eq. (7.37) or Eq. (7.36), one can derive a scaling law for the critical charge (taking

x = y = L)

∼ L

. (7.38)

For a sensitive volume size x × y = 100 µm

(x = y = 10 µm) one ﬁnds from

Eq. (7.37):

= 0.016 pC. (7.39)

This occurs according to JEDEC: Joint Electron Device Engineering Council, the Semiconductor

Engineering Standardization Body of the Electronic Industries Alliance (EIA).

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Displacement Damage and Particle Interactions in Silicon Devices 575

It is interesting to note that the number of electrons, N

, in the sensitive volume

corresponding to this critical charge is:

0.016 × 10

−12

1.6 × 10

−19

= 10

, (7.40)

where the factor 1.6 × 10

−19

C is the electronic charge. For a sensitive volume of

smaller size, x = y = 50 nm and d = 10 nm, one ﬁnds Q

= 0.04 fC and the corre-

sponding number of electrons is N

= 250. This shows that the concepts of critical

charge is not necessary applicable to circuit with very small sensitive volume. The

critical charge depends on the circuit voltage [Eq. (7.36)] and in principle on the

chip temperature. As the voltage drops, the amount of charge needed to induce

the bit ﬂip decreases and the circuit becomes more sensitive to upsets. Measure-

ments of upset rates have been performed in various conditions, underground, at

ground and above ground levels, varying the pinch voltage, which is the voltage

reduction from the nominal full operating voltage of the chip. As the pinch voltage

is increased, i.e., the chip operating voltage is decreased, the chips are seen more

sensitive to ionizing radiation (Figures 6 and 7 in [O’Gorman et al. (1996)]). The

dependence of Q

on temperature is expected to come from the dependence of

the charge carrier mobility on temperature [Eq. (6.70)]. The increase of mobility

with temperature translates into an increase of the chip gain as the charge are

moving faster to the collecting nodes. The increase of Q

with temp erature should

mean a better hardness of the chip to soft errors at large temperature. However,

experimentally, no signiﬁcant change in the upset cross section as a function of

temperature is observed for a series of bipolar SRAM chips (Table 7 in [Ziegler et

al. (1996)]), although the calculated critical charge for the same chips increases by

∼ 40% for a temperature increase from 50

◦

C to 120–130

◦

C (Fig. 11 in [Ziegler

et al. (1996)]). This again shows the critical charge as a rather crude parameter,

however very useful to compare relative chip upset rates.

From the deﬁnition of LET [Eq. (7.33)], the energy deposited, E

dep

, by a particle

along a path of length l through the sensitive volume of the device of density ρ is:

dep

= LET ρ l, (7.41)

if one assumes that LET and ρ are constant over the distance l. The corresponding

deposited charge is then given by

dep

ion

q, (7.42)

where E

ion

(= 3.62 eV in silicon, Table 7.1) is the average energy to create an

electron-hole pair, q is the electronic charge.

The LET of a particle can be related to its charge dep osition per unit path-

length. For a particle traversing silicon, the conversion factor between charge and

energy is

ion

= 22.6 MeV/pC.

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576 Principles of Radiation Interaction in Matter and Detection

Then, one can calculate the equivalent charge transfer rate

LETρ

ion

LETρ

22.60 MeV/pC

For instance, a LET of 97 MeV cm

−1

corresponds to a charge deposition of

1 pC/µm in silicon. Using Equation (7.41), the charge deposited in the sensitive

volume of the device along the path l can be expressed as a function of the LET of

the particle:

dep

LETρ l q

ion

. (7.43)

The critical charge, corresponding to a linear transfer threshold LET

, is then given

(in silicon) by

dep

= 0.01 × LET l [pC]. (7.44)

l is expressed in µm in Eq. (7.44). If one applies the RPP approximation to the

sensitive volume with size x × y and thickness d (Fig. 7.11), one ﬁnds that the

maximum path-length of the particle inside the volume, l

max

, is given by:

max

+ y

+ d

. (7.45)

Taking LET at the threshold value, LET

, i.e., the minimum LET required to

cause a SEU, one can express the critical charge in silicon as

= 0.01 × LET

max

[pC]. (7.46)

max

and LET

are expressed in µm and MeV cm

−1

, respectively, in Eq. (7.46).

Conversely, for exp erimental purpose one use LET

given by

LET

= 97 ×

max

[MeV cm

−1

] (7.47)

with Q

and l

max

expressed in pC and µm units, respectively.

A SEU occurs if Q > Q

which corresponds in the case of indirect ionization to

a nuclear recoil energy, E

, of

> 0.226 × LET

l [MeV]. (7.48)

A particle of given LET must traverse a minimum path, l

min

, in order to deposit

enough energy to induce an upset. From Eq. (7.47) one ﬁnds in silicon:

min

ion

q ρ LET

= 97 × Q

LET

[µm], (7.49)

where one uses the maximum stopping power (in MeV for any particle in the envi-

ronment. As seen earlier, the galactic cosmic ray environment has a component of

very high energy ions with large ionizing power due to their high charge. The ﬂux

of heavy ions is dominated by iron (Z = 26) for LET ∼ 27 MeV cm

−1

. Equa-

tion (7.49) becomes for silicon

min

= 3.60 × Q

[µm/pC]. (7.50)

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Displacement Damage and Particle Interactions in Silicon Devices 577

The dependence of LET

or Q

on the path length of the particle inside the

sensitive volume of the device shows the importance of considering the angle of

incidence, θ, of the incoming particle upon the device (Fig. 7.8) [Dodd, Shaneyfelt

and Sexton (1997)]. This is particularly important for devices of large size (x × y)

compared to their thickness (d). Deviation from normal results into the increase of

the path-length, l/ cos θ, inside the sensitive volume. An eﬀective LET is deﬁned as

LET

eﬀ

LET(θ = 0)

cos θ

. (7.51)

The angle at which a SEE may occur for a given LET is the critical angle, θ

, and

is deﬁned as

cos θ

LET

. (7.52)

The particles that generate upset have an angle of incidence between θ

and

. From this deﬁnition if LET > LET

, then all incident angles induce SEE. In

the case of LET < LET

, there must be a critical angle above which SEE oc-

curs [Binder (1988); Pickel (1996)]. In the case of incident protons and neutrons,

the critical charge corresponds to a energy threshold.

7.2.8 SEE Cross-Section

The sensitivity to each type of SEE (SEU, SEL, SEB,. . . ) in a device is estimated

from the measurement of the cross section, σ, as a function of LET for ions (Z ≥

2). By counting the number of SEE and knowing how many particles passed through

the device, one can calculate the probability of a given particle to cause a SEE. This

resulting number, which is the number of upsets divided by the number of particles

0 25 50 75 100 125 150

sat

Cross section (cm )

−1

LET (MeV cm mg )

LET

Fig. 7.12 Example of typical upset cross section curve as a function of LET (from [Leroy and

Rancoita (2007)]). LET

is the LET threshold for the device. σ

sat

is the saturation cross section

and corresponds to the lateral size of the device in the RPP approximation. The shape of the curve

is described by a Weibull distribution (see text).

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578 Principles of Radiation Interaction in Matter and Detection

per cm

causing the upset, is the cross section of the device. One can express this

cross section as:

σ(LET) =

events

[cm

], (7.53)

where Φ is the total incident ion ﬂuence (ions/cm

) on the device. For protons or

neutrons, the cross section is measured as a function of the energy E of the incident

protons or neutrons, i.e.,

σ(E) =

events

[cm

], (7.54)

where Φ is the total incident proton or neutron ﬂuence (protons/cm

neutrons/cm

) on the device. In both situations N

events

is the number of SEE events

counted during the exposure to the incident ﬂux. The SEE cross section may be

expressed per bit or p er chip:

σ(per bit) =

events

chip

bits/chip

, (7.55)

σ(per chip) =

events

chip

. (7.56)

The error rate (SEE) can be expressed as:

error rate =

events

device day

. (7.57)

One preferably uses the FIT (Failures-in-Time) rate value to characterize the be-

havior with time of a device under exposure. The value of the FIT rate is expressed

as the rate of error or failure of a device per billion of working hours, i.e, as

FIT = number of errors/(10

hours device). (7.58)

Then, a soft error rate of 1 FIT means that the mean time before an error occurs

is a billion device hours. It is frequent to have reported a FIT per Mbit:

1 FIT/Mb = 1 upset/10

hours/10

bits

= 1 × 10

−15

upset/(bit hours). (7.59)

In the case of a monoenergetic beam of one single type ion incident normal to

the surface of the device, σ measures the LET-dependent SEU sensitive area on the

chip. For the RPP approximation, the lateral dimensions of the chip are obtained

from the measured cross section, assuming a squared surface:

x = y =

√

sat

number of bits

. (7.60)

It is assumed that there is one sensitive volume per bit, and the shape of the cross

section for a given chip (Fig. 7.12) rising from a threshold to a saturation value is

understoo d as the composite response of multiple types of sensitive volume with

diﬀerent thresholds and features. Contrary to the case of direct ionization, for SEEs

generated by indirect ionization, it is not possible to interpret the measured cross

section in terms of sensitive area of the chip since the cross section convolutes the

probability of nucleon–nuclear interaction and the probability that the interaction

products recoil will achieve the charge density at various locations in the device

needed to induce a SEE.

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Displacement Damage and Particle Interactions in Silicon Devices 579

7.2.8.1 Calculation of SEU Rate for Ions

An ion (Z ≥ 2) traversing a semiconductor will loose its energy via ioniza-

tion. The energy deposition along the ion path will generate electron-hole pairs

in the semiconductor-based device (direct ionization, Sect. 7.2.7.1). When the ion

path crosses a region close to a sensitive node of a circuit (e.g., a p − n junction

in a memory cell) the collected charge at the node, if larger than a critical value

), may induce a SEE. The SEE rate calculation usually assumes a sensitive vo-

lume model based on the RPP approximation. In this approximation, the sensitive

volume is a rectangular parallelipipeded (Sect. 7.2.7.4). The incident ions are very

energetic and have very long ranges compared to the typical dimensions of the sen-

sitive volume. Equations (7.33, 7.42) can be used (in practice with TRIM [Ziegler,

Biersack and Littmark (1985b); Ziegler (2001, 2006)]) to estimate the deposited

energy by the ions, E

dep

, across the distance l, assuming a continuous slowing down

and a linear trajectory.

The probability to trigger an upset is the probability to have a deposited energy

larger than the critical energy E

of the device component and the probability to

have an upset is:

SEU

d Φ(LET)

d LET

[> l(LET)], (7.61)

where 1/Φ

×(d Φ(LET)/d LET) is the diﬀerential ion ﬂux spectrum as a function

of LET, i.e., the probability to encounter an ion with a given LET, Φ

is the

integrated ion space environment ﬂux and P

[> l(LET)] is the probability that this

particle covers a distance l(LET) such that the deposited energy E

dep

> E

or the

integrated path-length distribution. From Equation (7.33), one ﬁnds

l(LET) >

ρ LET

. (7.62)

Then, the upset rate, N

SEU

, is expressed as a function of the incident LET

spectrum and the path-length distribution [Bradford (1980)]:

SEU

LET

max

LET

min

d Φ(LET)

d LET

[> l(LET)] d LET, (7.63)

where A is the device total surface area [length: x, width: y (size S = xy), thickness:

d, A = 2 (x y + x d + d y)], LET

min

and LET

max

are the minimum LET (= LET

to produce an upset) and the maximum LET (∼ 10

MeV cm

−1

value which

corresponds to SEE immunity [LaBel (1993)]) of the incident particles distribution,

respectively.

The RPP approach can be improved by folding the LET spectrum with the

experimental cross section to account for sensitivity variations across the device. The

critical LET (LET

) of the sensitive nodes are not the same, but form a distribution

that can be ﬁtted by a Weibull function [Eq. (7.68)]. The integrated RPP (IRPP)

approach is used to take into account the variation of sensitivity by integrating over