Rate predictions for single-event effects-critique II

Abstract

The concept of charge efficacy is introduced as a mea-sure of the effectiveness of incident charge for producing single-event upsets. Efficacy is a measure of the single-event upset (SEU) sensitivity within a cell. It is illustrated how the efficacy curve can be determined from standard heavy-ion or pulsed laser SEU cross-section data, and discussed how it can be calculated from combined charge collection and circuit analysis. Upset rates can be deter-mined using the figure of merit approach, and values determined from the laser cross-sections or from the mixed-mode simulations. The standard integral rectangular parallel-piped (IRPP) method for upset rate calculation is re-examined assuming that the prob-ability of upset depends on the location of the hit on the surface. It is concluded that it is unnecessary to reformulate the IRPP ap-proach. Index Terms—Figure of merit (FOM), heavy ion, picosecond pulsed laser, proton, SEU rates, single event simulation, single event upset (SEU).

Full text

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2158 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 52, NO. 6, DECEMBER 2005
Rate Predictions for Single-Event Effects—Critique II
E. L. Petersen, Senior Member, IEEE, V. Pouget, Member, IEEE, L. W. Massengill, Fellow, IEEE,
S. P. Buchner, Member, IEEE, and D. McMorrow
Abstract—The concept of charge efficacy is introduced as a mea-
sure of the effectiveness of incident charge for producing single-
event upsets. Efficacy is a measure of the single-event upset (SEU)
sensitivity within a cell. It is illustrated how the efficacy curve can
be determined from standard heavy-ion or pulsed laser SEU cross-
sectiondata,anddiscussedhowitcanbecalculatedfromcombined
charge collection and circuit analysis. Upset rates can be deter-
mined using the figure of merit approach, and values determined
from the laser cross-sections or from the mixed-mode simulations.
The standard integral rectangular parallel-piped (IRPP) method
for upset rate calculation is re-examined assuming that the prob-
ability of upset depends on the location of the hit on the surface.
It is concluded that it is unnecessary to reformulate the IRPP ap-
proach.
Index Terms—Figure of merit (FOM), heavy ion, picosecond
pulsed laser, proton, SEU rates, single event simulation, single
event upset (SEU).
I. INTRODUCTION
S
rates in space environments; and to provide approaches for
producing devices with improved SEU characteristics. This
paper reexamines some of the basic concepts of previous SEU
studies.
In an ideal scenario, the measured error cross-section curve
for an array of identical cells (e.g., a memory) is a step function
at the critical LET for cell upset. However, observed cross-sec-
tion curves often exhibit significant curvature in the region ap-
proaching critical LET. One classical interpretation is that the
general shape of SEU cross-sectioncurvesarises from inter-cell
variations in the SEU susceptibility [1]. This interpretation is
certainly the case in circuitry that is nonregular, such as logic.
However, in the case of memories, such as SRAMs or DRAMs,
significant recent experimental data implicates the role of intra-
cell, rather than inter-cell variations. We examine anew the con-
ceptofcross-section,asobservedinmoderntechnologies,based
on this perspective.
Further, the standard integrated rectangular parallel piped
(IRPP) method for upset rate calculation, which is commonly
INGLE EVENT UPSET (SEU) studies have two basic
goals: to provide accurate methods of predicting upset
Manuscript received July 8, 2005; revised August 26, 2005.
E. Petersen is at 17289 Kettlebrook Landing, Jeffersonton, VA 22724 USA
(e-mail: epetersen3@earthlink.net).
V. Pouget is with the IXL-CNRS UMR, 3405 Talence cedex, France (e-mail:
pouget@ixl.fr).
L. Massengill is with Vanderbilt University, Nashville, TN 37203 USA
(e-mail: lloyd.massengill@vanderbilt.edu).
S.P.BuchneriswiththeQSSGroupInc./NASAGSFC,Greenbelt,MD20771
USA (e-mail: sbuchner@pop500.gsfc.nasa.gov).
D. McMorrow is with the Naval Research Laboratory, Washington, DC,
20375 USA (e-mail: mcmorrow@ccs.nrl.navy.mil).
Digital Object Identifier 10.1109/TNS.2005.860687
used today, is derived from the erroneous assumption that the
upset probability is a function of an homogeneous sensitive
volume, and that any nonideal shape of the cross-section curve
is a function of cell-to-cell variation in the critical charge.
In this paper we address the implications of variations in the
SEU sensitivity within a cell. This variation can be described
as a position-dependent internal SEU gain, or efficiency. How-
ever, because these terms are used elsewhere in circuit design,
and because the terminology “charge-collection efficiency” has
specific historical and mechanistic implications, we introduce
the term “efficacy”. The intent here is to use a term that is ap-
plicable across all technologies, irrespective if the “gain” is less
than or greater than unity.
Inwhatfollowsweintroducetheconceptofefficacybyexam-
ining how it can be determined from cross-section curves. This
leads to efficacy probability curves, and shows how the efficacy
contribution can be plotted as a function of fractional sensitive
area. The efficacy curve can also be determined from pulsed
laserorionmicro-beammeasurements,orfromcomputersimu-
lation.Wepresentasetoflasermeasurementsandillustratehow
to derive the cross-section versus linear energy transfer (LET)
and efficacy curves from this data. These curves in turn provide
theinformationnecessarytocalculatetheSEUsensitivity ofthe
device as given by the figure of merit (FOM). We examine the
rangeofvalidityofthismethodandconcludethatitmaybevalid
over eight orders of magnitude of space-upset rates for geosyn-
chronous orbit.
The standard method for error rate calculation, the IRPP ap-
proach, is re-examined assuming that the probability of upset
depends on the intra-cell, instead of inter-cell variation of the
charge deposition. By using this approach, two of the funda-
mentalassumptionsofthestandardRPPcalculationarerelaxed.
Yet, it is found that the error-rate expressions derived from the
new and classical approaches are consistent.
The concept of efficacy appears to explain often-observed
moderate LET behavior of cross-section curves in the vicinity
of the critical LET. The internal fields of the device lead to a
physically-based log normal cross-section curve. Efficacy does
notsupportthenonphysical-highefficacyvaluesatlowLETthat
are implied by extrapolation from high LET behavior.
Theorganizationofthepaperisasfollows.SectionIIreviews
the classic SEU models and indicates how they have changed
from a belief in the cross-section curve as due to inter-cell vari-
ation to the current belief in intra-cell variations. Section III
expands the concept of efficacy. Section IV relates efficacy to
SEU cross section curves and demonstrates how to determine
the fractional area of a device with a given efficacy. Section V
describes a laser experiment that determines the SEU efficacy
andcrosssectioncurvesanddemonstrateshowtheycanbecom-
0018-9499/$20.00 © 2005 IEEE

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PETERSEN et al.: RATE PREDICTIONS FOR SINGLE-EVENT EFFECTS—CRITIQUE II 2159
bined with the FOM model to determine SEU sensitivity. Sec-
tion VI makes the important point that combined charge col-
lection and circuit modeling can lead to device cross sections
and therefore to calculations of SEU sensitivity. Section VII
discusses how the concept of efficacy explains the low LET be-
haviorofSEUcrosssectiondata.SectionVIIIreviewstheFOM
and how it can be used with calculated efficacy or cross sections
curves to determined upset rates for a large range of devices and
orbits. SectionIXstudiestheimpactofintra-cellvariationofef-
ficacy on the IRPP rate calculations and concludes that the stan-
dard IRPP calculations are still valid. Section X summarizes the
paper.
II. CLASSICAL SEU MODEL
The fundamental assumption of classical SEU models is that
thereisasensitivevolume(SV)withinacircuitelementthatcan
collect charge generated by the passage of a heavy ion [2]–[9].
An SEU occurs when the electrical disturbance in the circuit
passes some critical threshold, which causes the circuit to re-
spond inan un-commandedway.Thechargegenerationisequal
to the product of the LET of the ion and a chord of the sensitive
volume. The most common models assume that the sensitive
volume has the shape of an RPP, and current procedures allow
for geometrical corrections due to the shape of the RPP. In the
RPP approach there is no dependence on the location or angle
of the hit except for the corresponding variations in path length;
charge generated anywhere in the SV is treated equally.
Initial SEU research was performed under the assumption
that there is a single unique charge for upset, the critical charge
. Initially it was believed that the shape of the SEU cross-
section curve was primarily determined by a spread of critical
charges from cell to cell inside a device [1]. In this interpre-
tation, the SEU cross-section reflects the fraction of cells that
upset at a given LET.
The above model is based on two important assumptions: 1)
the LET dependence of measured cross-section curves depends
primarilyoncell-to-cell variationsin sensitivity,and 2)theSEU
response for an ion with a given incident LET does not depend
on the specific location of the charge deposition within the cell.
The first assumption implies that a low cross-section point on
the curve corresponds to upsets in only a limited number of
cells. The experiments of Cutchins et al. [10] and Buchner et al.
[11] demonstrate that this is not the case. Cutchins’ experiment
show that a point on the low cross-section portion of the curve
reflects low cross-section contributions from all the cells, while
Buchner’sexperimentillustratesthatallcellshavethesamecrit-
ical charge for upset. It now appears that there is no support for
the concept of critical charge variation from cell to cell across
the chip being primarily responsible for the shape of the SEU
cross-section curves.
In contrast, a great deal of evidence has accumulated in sup-
port of the concept that the variation of cross-section with LET
commonlyobservedisduetovariationswithinthecell,although
much of this evidence was obtained while pursuing other ques-
tions, and was not viewed in this light. Early work in this area
is summarized in [12], [13]. Evidence has continued to accu-
mulate on more recent technologies. A series of pulsed laser
experiments has examined SEU onset thresholds in hardened
and unhardened CMOS parts; all parts tested exhibit signifi-
cant intra-cell variations in the SEU threshold [14]. Detchev-
erry,etal.wereabletoreproducetheexperimentalcrosssection
curveusingposition-dependent3Ddevicesimulationofasingle
cell [15]. Warren et al. [16] demonstrated the hit-location vari-
abilityofMOS/SOIdevicesthrough2Ddevicesimulations,and
Musseau, et al. later verified the effect experimentally through
laser probing [17]. Very recent work 2D measurements demon-
strate clearly the position-dependence of the SEU response for
a recent-generation, SEU hardened SRAM [35].
It appears that all semiconductor technologies involve some
combinationofgeometry,chargecollection,andchargeamplifi-
cationsuchthatthedevicesensitivityvariesacrossanindividual
transistor and within a single cell [12]. This appears to be the
primary origin for the characteristic shape of the cross-section
versus LET curve.
The concept of a range of critical charge was combined with
the rectangular parallelepiped (RPP) approach to upset rate cal-
culation to form the integral RPP calculation (IRPP) [18], [19],
[1]. This was done by an integration of RPP contributions with
the critical charge distribution indicated from the cross-section
variation. As it became clear that the charge collection response
variedacrossthecell,italsobecameclearthatthecriticalcharge
was a single value that was a circuit parameter only [20], [9].
The IRPP integral is now performed as a folding together of a
curve representing the upset rate as a function of LET, for the
RPPdevicegeometry,withtheprobabilityofupsetasafunction
of LET determined by the cross-section curve. This has become
the standard approach for upset-rate calculation in the space en-
vironment.
III. CROSS-SECTION AND EFFICACY CURVES
In Section I, we introduced the concept of efficacy for
describing the efficiency of charge collection for predicting
upset rates. Efficacy is the correlation between single-event
(SE) strike locations and actual upset sensitivity—i.e., it relates
physical device geometry to the circuit response. We now
attempt to quantify this relationship.
It is assumed that there is a unique critical charge for upset.
This is the charge needed at the next circuit node for reset. The
critical charge corresponds to the product of the LET at 50%
of the limiting cross-section and the device nominal depth [1]
(using the conversion factor of 1 pC/
The limiting cross-section is the saturation value as indicated
by a log normal or Weibull fit to the data. Assume that the
SEU Efficacy is one when the cross-section is 50% of the lim-
iting cross-section
. We define the SEU efficacy value as
and assume constant depth. Therefore, it varies as
1/LET.
The definition is not circular. There are three different quan-
tities involved [9]: (1) the charge deposited by the ion; (2) the
charge that is produced and presented to the next circuit node;
and (3) the critical charge that is necessary at the next circuit
node in order to produce an upset.
IfanupsetisproducedatanLETthatisonehalfof
the critical charge is being developed from charge deposition
MeV/mg/cm ).
,then

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2160 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 52, NO. 6, DECEMBER 2005
Fig.1.
describe it. The plot also shows the efficacy as a function of the LET.
IDT71256(R-MOS)cross-sectiondatawiththelognormalcurvesthat
that is one half of the circuit critical charge (one-half LET, same
depth). Therefore, the efficacy for this hit is two. If an upset
is produced at an LET that is twice
twice the critical charge must be deposited to produce an upset
(twice the LET, same depth). Therefore, the efficacy for this hit
is one-half. Hits at this location by ions of lower LET will not
produce an upset.
The efficacy and cross-section curves are perhaps better rep-
resented by the cumulative log-normal distribution than by the
Weibull distribution because the log-normal distribution can be
related to the device physics [20]1. The log-normal function is
the normal distribution with the variable being LET. Let:
, which means that
where
the standard deviation of the function in terms of ln(LET). The
log normal distribution is:
of the function in terms of ln (LET) andis
The cumulative log normal distribution is:
IV. SEU EFFICACY AS A FUNCTION OF AREA
The efficacy behavior of a device can be examined starting
with the cross-section versus LET curve. One can convert the
cross-section data as a function of LET to cross-section as
a function of the efficacy. This is a cumulative log-normal
function (or integral Weibull function). We can invert the plot
to obtain the efficacy as a function of area. Fig. 1 shows the
basic measured cross-section curve for the R-MOS IDT 71256
1Note that the log-normal function contains one less parameter than the
Weibull curve. When used to describe cross-section curves, the log-normal
is sometimes poorer at low LET. Some devices act as if there is a cutoff at
high efficacy; others show a large (relative) contribution at high efficacy. The
calculated upset rate will be 1–2% larger or smaller if the Weibull distribution
is used to describe the cross-section curve, instead of the log-normal function.
This is discussed in Section VII
Fig. 2.
of the cross-section curve plotted against efficacy rather than LET.
The IDT 71256 efficacyprobability curve. This is the differential form
Fig. 3.
the efficacy value. If this curve is measured or calculated, it can be transposed
to show the cross-section as a function of LET. The LET at 25% of the limiting
cross-section can be determined from this curve and used directly to determine
upset rates using the figure of merit approach.
IDT 71256 efficacy as a function of the relative area that contributes to
SRAM [1], [21], together with its differential form. The older
device used here provides a clear example of this approach.
The approach is equally valid for modern devices, although
the results can be more complex [9]. For the purposes of this
development, the efficacy is defined to be unity at the 50%
point of the cross-section curve (designated
its value elsewhere determined by the ratio of the LET to
This is shown in Fig. 1.
Fig. 2 shows the efficacy probability curve obtained by plot-
ting the differential cross-section curve versus the calculated ef-
ficacyforthelog-normaldistribution.Thewidthofthecurvecan
vary greatly for different technologies. Note that one approach
to hardening devices is to narrow the efficacy probability curve
so that there is less contribution from the high efficacy side.
The concept of efficacy can be used for any technology. If a
circuit designer can determine the efficacy distribution for his
device, he can calculate the SEU rate for his device. Methods
of determining the efficacy distributionare discussed in the next
twosections.Therelativeareasthatcontributetotheefficacycan
be determined from the normalized cross-section as a function
of efficacy, as is shown in Figs. 3 and 4. Fig. 4 shows the plot on
a log scale, and demonstrates that the high efficacy contribution
) and to have
.

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PETERSEN et al.: RATE PREDICTIONS FOR SINGLE-EVENT EFFECTS—CRITIQUE II 2161
Fig. 4.
areas that contribute to high efficacy values.
The IDT 71256 data shown on a log plot to show the relatively small
comesfromaverysmallfractionofthedevicearea.Theefficacy
is greater than 5 for only 2% of the total area.
Each given technology generally has curves that group to-
gether. There is a large variation between technologies. The ef-
ficacy in this example approaches 10. Even larger efficacy oc-
curs in devices in which diffusion is likely to be present [13].
Bulk and SOI CMOS devices generally have maximum effica-
cies less than 10.
V. EFFICACY AND SEU SENSITIVITY DERIVED FROM A PULSED
LASER SEU EXPERIMENT
A series of pulsed-laser experiments have been performed
to illustrate the variation of SEU sensitivity across one device.
We obtain a cross-section and, from that, determine the efficacy
andinformationnecessaryforFOMcalculations.Becauseofthe
largefeaturesizeofthisdevice,itprovidesanexcellentexample
of the approach.
A. Laser Experiment
Pulsed laser SEU measurements have been performed on a
5 V HM-6504, 4 K CMOS RAM at the IXL laser facility [22]
using 1 ps, 800 nm optical pulses with a spot size of 1.1
at the surface of the device. The HM-6504 was first tested for
single event upsets in 1979, before systematic measurements of
cross-section curves were common [23].
A single memory cell, the “target” cell, is visually selected
in the middle of the array. Its logical address is read from the
memorytesterbyinducinganSEUwiththelaser.Theaddresses
of the surrounding cells, the “neighbors”, are obtained in the
same way. In order to increase the test speed, the tester checks
only the target cell and its eight neighbors.
Arectangularscanareaisdefinedaroundthetargetcellsothat
it includes all the SEU sensitive regions for this address. Since
this area slightly overlaps the neighbors, the laser may also flip
them. During the laser scan, after each laser strike: 1) only up-
sets detected in the target cell are used to build the sensitivity
mapping; and 2) the state of neighboring cells is monitored to
ensure that the electrical environment of the target cell remains
the same.
m
Fig. 5.
the HM-6504 with 4 pJ, 800 nm optical pulses. At this pulse energy there is
only one pixel with high efficacy so that the hit causes an upset. No upsets are
observed for 0 to 1 transitions.
Laser-induced upsets for 1 to 0 (left) and 0 to 1 (right) transitions of
Fig. 6.
the HM-6504 with 7.2 pJ, 800 nm optical pulses.
Laser-induced upsets for 1 to 0 (left) and 0 to 1 (right) transitions of
The2DSEUmapisobtainedbyscanningthedeviceinanx-y
grid with 1 m resolution. A single laser pulse fired at each grid
point, with each detected SEU recorded as a black spot at the
corresponding location. The same area is scanned with pulses
of increasing energy from 3 pJ to 60 pJ for both all-to-0 and
all-to-1 test patterns. Figs. 5–8 show representative results. At4
pJ,thereisonlyonepixelwithsufficientlyhighefficacytocause
a 1 to 0 upset; no upsets are observed for 0 to 1. For the 0 to 1
pattern, the first transitions occur at 7.2 pJ (Fig. 6). As the en-
ergy increases, more and more locations have sufficient efficacy
to produce upsets. These figures clearly illustrate that the sensi-
tive area inside the cell increases with the quantity of deposited
charge [11]. The experiment was repeated for several different
target cells with analogous results. No latch-up is observed for
incident laser pulse energies below 150 pJ. A similar series of
plots have been produced using a microbeam by Dodd et al.
[24]. They did not carry their results on to a cross-section curve.
In order to calculate the FOM, laser data have to be corrected
for several effects, and the laser energy has to be calibrated into
an equivalent LET.
B. Laser Cross-Section
The total number of hits
and each pattern. A single hit corresponds to the smallest sen-
sitive area
that can be measured, which is determined by the
scanning step size. In this test, a sensitive area of 1 m is asso-
ciatedwitheachhit.Thiselementaryareagivestheresolutionof
themeasurementandcanbeseenastheinverseofthelaserpulse
fluence on the scanned area [25]. The measured laser cross-sec-
tion is thus given by
.
Fig. 9 shows the results as cross-section versus laser pulse
energy. It is necessary to make several corrections to the raw
data. The first is associated with the increase in the “effective”
spot size with the pulse energy. An increase of the pulse energy
is recorded for each energy level

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2162IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 52, NO. 6, DECEMBER 2005
Fig. 7.
with 10.4 pJ, 800 nm optical pulses.
Laser-induced upsets for 1 to 0 (left) and 0 to 1 (right) of the HM-6504
Fig. 8.
with 20 pJ, 800 nm optical pulses.
Laser-induced upsets for 1 to 0 (left) and 0 to 1 (right) of the HM-6504
does not change the radial width parameter of the Gaussian dis-
tribution of the beam intensity, but it does change the height of
this distribution. Thus, the range over which the laser intensity,
or equivalently the generated carrier density, is above a given
threshold increases with the pulse energy. This effect leads to
an over-estimation of the cross-section. As a first order approx-
imation, if we consider that the sensitivity can be described by a
threshold carrier density, this effect can be corrected using [26]:
where E is the laser pulse energy,
ergy,
is the beam waist, and
section. The resulting corrected average cross-section curve is
shown in Fig. 9 labeled “beam”.
Another effect that has to be taken into account is the metal
interference that prevents the laser light from reaching the sil-
icon. Since some of these areas may be sensitive to upset but
will not be counted as such, the metal interference effect leads
toan under-estimationof thecross-section. Thiseffectis clearly
visible on Figs. 7 and 8 where black pixels surround metal lines
(clear structures). For VLSI devices, this effect is problematic
and can require backside testing [27], [28]. In the present case,
image processing of a microphotograph of a memory cell re-
veals that approximately 30% of the cell area is covered by
metal. Again using a first order correction, we assume that the
sameratioappliestothesensitiveareas,meaningthat30%ofthe
sensitive areas are not detected by the laser test. The resulting
corrected average cross-section curve is plotted on Fig. 9 (beam
and metal). This curve shows connected points. Fig. 13 (vide
infra) shows the data fitted with a log-normal distribution.
The laser cross-section curves of Fig. 9 do not show a clear
saturation, even when corrected for the effective beam size ef-
fect. However, from the 60 pJ distribution shown in Fig. 10, a
geometricalestimationofthelimitingcross-sectionrequiredfor
is the SEU threshold en-
is the measured cross-
Fig. 9.
average values correspond to the heavy ion cross-section measurements made
using a checker-board pattern.
Laser cross-section results calculated from data of Figs. 5–8. The
Fig.10.
with 60 pJ, 800 nm optical pulses. The estimation of the limiting cross-section
is indicated.
Laser-inducedupsetsfor1to0(left)and0to1(right)oftheHM-6504
the FOM calculation is obtained. This gives
for the average between both tested patterns.
cm
C. Energy Calibration
In recent years considerable success has been attained in
correlating experimentally determined SEU and SEL threshold
LET values for pulsed-laser and heavy-ion measurements [14],
[29]. Particularly good correlation has been observed for bulk
and epi CMOS parts, with a correlation factor of
MeV cm /mg for nominally 590 nm optical excitation found
to be accurate for a wide range of part types. To use this
correlation factor for the present measurements, which were
performed at800nm, it is necessaryto correctfor thedifference
in wavelength. This can be accomplished using wavelength-de-
pendent SEU measurements on a Si SRAM [30]. Using the data
in Fig. 6 of [30] at 600 nm and 800 nm gives a scaling factor of
0.49 between these two wavelengths, resulting in an LET/laser
correlation factor of
MeV. cm /mg for 800 nm.
D. Laser Efficacy and FOM
From Fig. 9, a laser pulse energy of 20 pJ corresponds to the
cross-sectionat50%ofthemaximum.Theefficacyisthengiven
as the ratio of that value to the energy deposition. Fig. 11 shows
the efficacy as a function of the relative area. We compare these
results with the efficacy curve for the IMS 1601, a MOS de-
vice, and with the 6504RH. We observe qualitatively very sim-
ilar curves.