Development of a Nuclear Reaction Database on Silicon for
Simulation of Neutron-Induced Single-Event Upsets in
Microelectronics and its Application
Yukinobu Watanabe , Akihiro Kodama , Yasuyuki Tukamoto and
Hideki Nakashima
Department
of Advanced Energy Engineering Science, Kyushu University,
Kasuga, Fukuoka, 816-8580, Japan
Abstract. We have developed a cross-section database for neutron-induced reactions on 28 Si in the energy range between
2 MeV and 3 GeV in order to analyze single-event upsets (SEUs) phenomena induced by cosmic-ray neutrons in microelectronic devices. A simplified spherical device model is proposed for simulation of the initial processes of SEUs. The model
is applied to SEU cross-section calculations for semiconductor memory devices. The calculated results are compared with
measured SEU cross sections and the other simulation result. The dependence of SEU cross sections on incident neutron
energy and secondary ions having the most important effects on SEUs are discussed.
INTRODUCTION
Radiation effects on microelectronic devices, e.g., singleevent upsets (SEUs), have been recognized as one of
the key reliability concerns for both current and future
integrated-circuit technologies, and the related subjects
are being studied extensively [1, 2]. Cosmic-ray neutrons
with a wide energy range from MeV to GeV are regarded
as one of the major sources of the SEUs in the devices
used on the ground or in airplanes. Microscopically, the
cosmic-ray-induced SEUs begin with the interaction of
energetic neutrons with materials in the devices, and then
light-charged particles and heavy ions can be generated
via a nuclear reaction with a silicon nucleus. They can
give rise to a local charge burst in a sub micron-size volume, which results in upsets of the memory cell information quantum. Therefore, the nuclear-reaction data to describe the probability of neutron interactions are highly
requested as a fundamental physical quantity necessary
for understanding the SEU phenomena and estimating
the SEU rate. To meet this demand, we have constructed
a cross section database for silicon, using two evaluated
nuclear data files (JENDL-3.3 [9] and LA150 [10]) and
QMD calculation [11], for neutron energies ranging from
2 MeV to 3 GeV. It has so far been applied successfully
to several SEU simulations [3, 4, 5, 6].
In the present work, we propose a simplified device model of calculating SEU cross sections based on
a Monte Carlo method, instead of our previous BGR
model [3]. Using the cross-section database and the
energy-loss calculation of secondary ions, one can simulate the initial SEU processes, i.e., generation of secondary ions via nuclear reactions and the initial charge
distribution induced in the device. A simplified spherical
device structure with only silicon layers is taken into account, and SEU cross sections are calculated on the basis
of the initial processes simulated in terms of a Monte
Carlo method. The experimental data for SRAMs and
the other simulation results for DRAMs are analyzed by
the present model calculations, with particular attention
to the generated secondary ions and the incident energy
ranges that have the most significant impact on SEUs.
CROSS-SECTION DATABASE
A nuclear reaction database for 28 Si was constructed by
combining the JENDL-3.3 [9] and LA150 [10] libraries
and the QMD calculation [11] in the energy range from
2 MeV to 3 GeV. The JENDL-3.3 library [9] was used to
obtain the double-differential cross sections (DDXs) for
light-charged particles (p and α ) and all recoils (24 25 Mg,
27 28 Al, and 27 28 Si) in the n+ 28 Si reaction for neutron
energies between 2 MeV and 20 MeV. The DDXs calculation of the recoils from the JENDL-3.3 library was
reported elsewhere [4]. The data for energies between
20 MeV and 150 MeV were taken from the LA150 library [10], in which the DDXs of all recoils are included, but the angular distributions are isotropic in the
laboratory system. The cross sections for energies above
CP769, International Conference on Nuclear Data for Science and Technology,
edited by R. C. Haight, M. B. Chadwick, T. Kawano, and P. Talou
© 2005 American Institute of Physics 0-7354-0254-X/05/$22.50
1646
150 MeV were calculated using the QMD [11] plus statistical decay model (GEM [12]).
In Fig. 1, the cross sections of elements produced
in the n + 28 Si reaction are plotted for three incident
energies, 10 MeV, 100 MeV, and 1000 MeV. It is seen
that secondary ions with a wide mass number range are
generated as the incident neutron energy increases.
incident neutron
n+Si reaction
Rc
4
10
1000 MeV
100MeV
10 MeV
H
3
Cross Section (mb)
10
He
2
10
B
1
Li
n+28Si
charge
collection
volume
Ne
C N O
10
Ri
secondary
ions
Na
F
Mg Al
FIGURE 2. Schematic illustration of the simplified spherical
device model.
Si
Be
0
10
Using our simplified model, the SEU cross section for
incident neutron energy, En , is given by
P
-1
10
0
2
4
6
8
10
12
14
16
j
σSEU En ∑ σSEU
En Atomic Number
FIGURE 1.
ments.
j
Production cross sections of secondary ele-
NSi
∑
j
A SIMPLIFIED MONTE CARLO MODEL
FOR CHARGE GENERATION AND
COLLECTION
We consider SEU events in a simplified spherical device consisting of silicon, as shown in Fig. 2. This device
model is similar to that used in [7]. The interaction and
charge-collection volumes are concentric spheres with
radii Ri and Rc , respectively. A nuclear reaction with silicon takes place in the interaction volume, and secondary
ions are generated and move in the device while slowing down. The energy deposited by a secondary ion into
the charge-collection volume is calculated using the data
of the range and energy loss obtained by the SRIM code
[13]. It is assumed that the whole charge (Q) generated
into the charge-collection volume is collected into a portion where the memory information is kept as charge,
and if Q is greater than the critical charge, Qc , then the
SEU happens eventually. In this model, the initial processes of the SEU event, namely, nuclear reactions with
the silicon nucleus and the following charge deposition
by the secondary ions, are taken into account properly,
while the transport calculation of the generated charge
by drift and diffusion processes is neglected and the size
of the charge-collection volume is introduced as a model
parameter, Rc .
dr
r Ri
QQc
d 2σ j
dE j dΩ j
dE j dΩ j (1)
where j denotes the kind of generated secondary ion,
NSi is the number density of the Si nucleus, and
(d 2 σ j dE j dΩ j ) is the double-differential production
cross section of the secondary ion j. In practical calculations, isotropic angular distribution is assumed for
emission of the secondary ion for simplicity; therefore
(d 2 σ j dE j dΩ j ) is replaced by d σ j dE j 4π in Eq. (1).
This assumption represents approximately a situation
where neutrons are incident into the device uniformly
from any direction. The three-fold integration over the
interaction volume and the energy and angle of the secondary ion in Eq. (1) is made using a Monte Carlo
method under the condition, Q Qc . The size of the
interaction volume, Ri , is determined by the condition
where the calculation converges.
Using the neutron flux, φ En , the cosmic-ray-induced
SEU rate is finally obtained by
SEU rate
σSEU En φ En dEn (2)
RESULTS AND DISCUSSION
Figure 3 shows a comparison of the calculation with
measured data [8] for SRAMs with 256 Kb or 1 Mb.
The measured data are normalized to the data of Cypress. One can notice that the energy dependence of the
measured SEU cross sections is nearly similar and the
magnitude alone depends strongly upon the devices. Accordingly, two parameters, Qc and Rc , were determined
1647
energy dependence of SEU cross sections, although it is
too simple to predict the magnitude precisely.
2
10
Qc=30 fC
DRAM
Rc=0.35 µm, Ri=7.0 µm
1
σseu(arb. unit)
so that the energy dependence of the measured data is
reproduced well, and the magnitude was finally normalized to the data of Cypress. The obtained best-fit values
are Qc =53 fC and Rc =1.0 µ m. The calculation with these
values shows satisfactory agreement with the measured
data over the whole neutron-energy range. The results
with different Qc and Rc are also presented in Fig. 3 to
see the sensitivities of these parameters to the calculation
results. All the calculations are normalized at 45 MeV for
comparison.
-12
10
10
0
10
(a)
Simulation (Kawakami et al.)
-1
10
Matra-H.(X 0.85)
Cypress(X 1.0)
Micron(X 2.1)
Toshiba(X 6.5)
NEC(X 7.2)
2
σSEU(cm /bit)
present work
-13
10
10
100
1000
Neutron Energy (MeV)
Rc=1.0 µm
Rc=0.5 µm
Rc=2.0 µm
FIGURE 4. Comparison of calculated SEU cross sections
with other simulation results [5] for a DRAM device with Qc =
30 fC. Both results are normalized at 100 MeV.
-14
10
0
20
40
60
80
100 120 140 160
Neutron Energy (MeV)
-12
10
Secondary ion
2
σSEU(cm /bit)
(b)
Matra-H.(X 0.85)
Cypress(X 1.0)
Micron(X 2.1)
Toshiba(X 6.5)
NEC(X 7.2)
-13
10
Qc=53 fC
Qc=40 fC
Qc=60 fC
0
20
40
60
80
50 MeV
100 MeV
1 GeV
0
-14
10
P
Si
Al
Mg
Na
Ne
F
O
N
C
B
He
100 120 140 160
Neutron Energy (MeV)
FIGURE 3. Comparison of calculated SEU cross sections
with measured ones [8] for SRAMs. The measured data are
normalized to the data of Cypress. The sensitivities of (a) Rc
and (b) Qc to the calculated results are shown.
Next, our calculation based on the present simplified
model is compared with a more realistic SEU simulation [5] for DRAM with Qc =30 fC in Fig. 4. The error
bars on the solid line stand for the statistical errors of our
Monte Carlo calculation. Both results are normalized at
100 MeV for comparison. Our nuclear reaction database
was also used in the latter simulation. Both calculations
show good agreement below 150 MeV, while our calculation is at most 20% smaller than the latter one above
150 MeV. This result may indicate that our simplified
model is useful in rough discussion about the neutron
5
10
15
20
25
Fraction (%)
30
35
FIGURE 5. Ratio of each secondary ion to total SEU cross
sections at En = 50 MeV, 100 MeV, and 1 GeV for the device
with Qc =30 fC shown in Fig. 4.
Figure 5 illustrates a trend that lighter reaction products such as C, N, and O contribute to SEU largely at
the highest incident energy of 1 GeV, while heavier reaction products such as Na, Mg, and Al are dominant
at 50 MeV. To see the range effect of these secondary
ions, the radial distributions of SEUs are plotted for O
and Mg as a function of the distance from the center of
the device at En =50 MeV and 1 GeV in Fig. 6. The contribution from the outer region far from the sensitive region becomes important for light-reaction products such
as O. This trend is appreciable as the incident energy
increases. Thus, it is found that the generation of lightreaction products in the long range affects SEUs predominantly at high-incident energies.
1648
-3
SEU distribution (µm )
10
This can be explained by the differences in the range and
linear-energy transfer of ions.
Nuclear reaction data for the elements except Si (e.g.,
B, N, O, Al, P, Ti, Cu, As, Ta, etc.) are also required for
more detailed SEU simulations. To meet the requirement,
an extension of the present nuclear-reaction database
is planned, and this task is to be accomplished in the
JENDL high-energy file project [14] that is currently in
progress.
5
10
4
10
3
10
2
10
1
10
0
(a)
En= 50 MeV
O
Mg
-1
10
ACKNOWLEDGMENTS
-2
10
0
2
4
6
8
10
-3
SEU distribution (µm )
R(µm)
10
5
10
4
10
3
En=1 GeV
10
2
O
Mg
10
1
10
0
The authors are grateful to Y. Kawakami and M. Hane
for valuable discussions and useful comments about SEU
simulations.
(b)
REFERENCES
1.
2.
-1
10
3.
-2
10
0
2
4
6
8
10
4.
R(µm)
FIGURE 6. Radial distribution of SEUs at En = 50 MeV and
1 GeV for a device with Qc =30 fC and Rc =0.35 µ m. The error
bars indicate the statistical errors included in the Monte Carlo
calculation.
SUMMARY AND CONCLUSIONS
5.
6.
7.
8.
For neutron-induced SEU simulations, the cross-section
database of 28 Si was constructed for incident energies
ranging from 2 MeV to 3 GeV by using the evaluated
nuclear data files (JENDL-3.3 and LA150) and the QMD
calculation. A simplified spherical device model was
proposed to simulate the initial processes, i.e., nuclear
reactions and the sequential charge deposit by secondary
ions, in the SEU effects. The SEU cross sections were
calculated using the Monte Carlo method, by introducing
the assumption that the SEUs occur if the initial charge
deposited by secondary ions in the charge-collection volume exceeds the critical charge. The calculated results
reproduced well the energy dependence of the measured
SEU cross sections and the other simulation result. From
the analyses, it turned out that heavy-reaction products
(Na, Mg, Al, etc.) have important contributions at lowincident energies but light reaction products (C, N, O,
etc.) become dominant with increasing incident energy.
9.
10.
11.
12.
13.
14.
1649
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