Methodology of Soft Error Rate Computation in Modern Microelectronics
G.I. Zebrev1, I.O. Ishutin1, R.G. Useinov2, V.S. Anashin3
1
Department of Micro- and Nanoelectronics, Moscow Engineering Physics Institute, Russia
2
Research Institute of Scientific Instruments, Lytkarino, Moscow region, Russia
3
Scientific Research Institute of Space Instrument Engineering, Moscow, Russia
35-WORD ABSTRACT:
We have proposed test methodology based on successive experimental determination of angular cross-section dependence followed be averaging over full solid angle. Equivalence between phenomenological and chord-length distribution
averaging for soft error rate computation is revealed.
Corresponding (and Presenting) Author:
Gennady I. Zebrev, Moscow Engineering Physics Institute, 115409, Moscow, Kashirskoye sh., 31, (Russia) phone:
495-3240184, fax: 495-3242111, email: [email protected]
R. G. Useinov is with Research Institute of Scientific Instruments, Lytkarino, Moscow region, Russia
O. Ishutin is a postgraduate of Moscow Engineering Physics Institute
V.S. Anashin is with Scientific Research Institute of Space Instrument Engineering, Moscow, Russia
Session Preference: Modeling and Simulations
Presentation Preference: Poster
I. INTRODUCTION
With the continuous scaling of technology node and decreasing of supply voltage, soft error issues have
emerged as a new design challenge. As has been noted in Ref.[1] a need arises “to rethink test methodologies,
procedures and models in order to predict the true behavior of these technologies in space”. In this report we
will attempt to describe some new approachs to test and prediction methodologies as applied to modern microelectronics.
II. CROSS-SECTION CONCEPT
It is well known that single event rate prediction is based on experimental cross-section versus linear energy transfer (LET). Cross-section can be defined in ambiguous manner [2-4]. Differential cross-section with
respect to primary particle flux can be defined as
d N ( Λ ;θ , ϕ )
(1)
σ ( Λ; θ , ϕ ) =
φ ( Λ; θ ,ϕ ) do d Λ
where is the solid angular element, d N ( Λ;θ ,ϕ ) is amount of errors due to particles with LET in the range
Λ ÷ Λ + d Λ , incident from the solid angular element do = d cos θ dϕ ( (θ , ϕ ) are polar and azimuthal angle
with respect normal to IC face, φ ( Λ;θ , ϕ ) [cm-2 sterad-1 (MeV-cm2/mg)-1] is differential fluence per LET unit
per solid angle. Knowing σ ( Λ;θ , ϕ ) and taking into account a definition we can compute full error number
immediately from definition (1)
N = ∫∫∫ σ ( Λ; θ , ϕ ) φ ( Λ; θ , ϕ ) d ( cos θ ) dϕ dΛ .
(2)
In general case one can introduce LET dependent cross-section σ ( Λ ) averaged on full solid angle 4π,
which is defined as
σ (Λ) =
1
4π
∫∫ σ ( Λ; θ , ϕ ) d ( cos θ ) dϕ .
(3)
Cosmic ray direction distributions and corresponding LET spectra are typically assumed to be isotropic
φ ( Λ ) = 4 π φ ( Λ;θ , ϕ ) . Then the general relation in Eq.2 reads
N = ∫ σ (Λ) φ (Λ) dΛ .
(4)
In this manner one needs a procedure of averaging over all direction of incident particles. There are at
least two approaches to such angular averaging.
II. PHENOMENOLOGICAL ANGULAR AVERAGING APPROACH
There is in principle a possibility to perform angular averaging directly measuring experimentally crosssections for a large number of particle flux directions. For example for mono-directional beam of particle
with a specified LET ( Λ ) and direction (θ 0 , ϕ 0 ) we have
φ ( Λ; θ , ϕ ) ≅ φ ( Λ;θ 0 , ϕ0 ) δ ( cos θ − cos θ 0 ) δ (ϕ − ϕ0 )
(5)
where φ ( Λ ) is total beam fluence with specified LET. Using Eq.1 or Eq.2 we have basic equation for experimental determination of single event cross-section angle dependence
N (Λ;θ 0 ,ϕ0 )
σ exp = σ (Λ;θ 0 ,ϕ0 ) =
φ (Λ;θ 0 ,ϕ0 )
2
(6)
where N (θ 0 ,φ0 ) is error number registered at a given angle and LET. This equation yields experimental angle dependence of single event cross-section with respect to, for example, a chip surface normal (this is no
more than convenient choice). Notice that no additional cosine arises in basic Eq.6.
Measuring in some detail the cross-section angular dependence, one can in principle perform (at least approximately) direct averaging over full solid angle.
σ exp ( Λ ) =
1
4π
+1
∫ dμ
2π
∫
−1
0
+1
dϕ σ exp ( Λ, μ , ϕ ) ≅ ∫ σ exp ( Λ, μ ) d μ ,
(7)
0
where μ = cosθ is a cosine of polar angle. In assumption of
cross-section independence on azimuthal angle the averaging is
reduced to integration of experimental dependence on μ. It is
equivalent to determination of a square under experimental curve
σ exp ( Λ, μ ) (see Fig.1).
Successive phenomenological approach does not require any
additional approximations. Unfortunately this approach is impossible in full measure because of economics consideration.
Fig.1. Illustrative sketch of cross-section polar angular dependence.
II. CHORD-LENGTH DISTRIBUTION AVERAGING APPROACH
Additional concepts of sensitive volume (SV) and critical energy EC should be involved due to lack of full
experimental information. Critical energy is closely connected with circuit parameter of critical charge QC
which is defined as minimum amount of released charge to upset a memory cell. Both the sensitive volume
(which is effective volume of charge collection) and critical charge are in essence circuit parameters depending on geometry, capacitance, transconductance etc. and can be computed in principle by circuit or TCAD
simulation. We have introduced in Ref. [5] the memory cell sensitivity function K ( Λ s − EC ) which is an error probability dependent on energy deposition overdrive.
In the sensitive volume approximation for isotropic flux the full angular averaging is equivalent to averaging over the differential chord length distribution. This allows to replace the angular averaging of unknown in
general phenomenological cross-section in Eq.3 by averaging of memory cell sensitivity function with a
known for a concrete sensitive volume shape the chord length distribution f(s)
σ (Λ) =
1
4π
∫∫ σ ( Λ; θ , ϕ ) d ( cos θ ) dϕ =
S0
4
smax
∫ K ( Λ s − E ) f ( s ) ds ,
C
(8)
0
where S0 is the full area of sensitive volume. Inserting Eq.8 in Eq. 4 one obtains
N = ∫φ (Λ)
smax
∫ K ( Λ s − E ) f ( s ) ds dΛ .
C
(9)
0
This is indeed computational relationship proposed in Ref.[5] and used in heavy ion simulator PRIVET
with the exact chord length distribution for rectangular parallelepiped sensitive volume.
III. DISCUSSIONS
We have in Eq.9 integration over two-dimensional “LET-chord length” domain with rather complicating
integrand. Typical view of integrand is shown in Fig.2. As can be seen from Fig.2-3 (the latter is the level
curve map version of Fig.2) there is the pronounced “optimal” region of the “LET-chord length” domain with
maximum contribution in soft error rate (see also Fig.1 in Ref.[5]). Phase curve (hyperbola) defined by equation EC = Λ s divide a domain in Fig.2 on two regions where conditional error probability ≅1 (upper-right re-
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gion, Λ s > EC) and where error probability ≅ 0 (lower-left region, Λ s < EC). Partial SER is determined by
full integrand in Eq.9.
Fig. 2. Partial contribution to SER as 2D function of chord length and LET
Fig. 3. Density plot of SER (light color corresponds to maximum
rate)
SER simulator PRIVET is one of computation modules of the program complex OSOT for SER prediction
in space environments which has been developed under the aegis of the “Roskosmos” (Russian Federal Space
Agency) for the establishing ITEP accelerator based test center [6]. An example of simulation with the OSOT
is shown in Fig.4.
@
Fig. 4. Comparison of OSOT simulation results with CREME96 and flight data adapted from Ref.[7]
Interrelations with between variety of existing computational schemes were discussed in Ref.[ 5]. We regard computational approach in PRIVET as taking mathematical advantage over traditional approachs but
having the same accuracy class since all of the approachs are based on the same physical approximations.
We intend to discuss in a full version of the report following issues:
•
Fundamental problem of SER computation is that the critical energy is the real sensitivity parameter of
memory cell while only the critical LET can be elicited from the experimental test.
•
Extension of PRIVET model for taking into account nuclear reactions.
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•
An explicit taking into account of straggling and Landau distribution for modeling of K (Λs − EC )
function spreading or, the same, cross-section vs LET curve.
REFERENCES
[1] N. Haddad et al. “Traditional Methods Shortfall in Predicting Modern Microelectronics Behavior in Space”
RADECS 2007 Proceedings.
[2] R. Koga, “Single-Event Effect Ground Test Issues”, IEEE Trans. on Nucl. Sci., V.43(2), 661-671 (1996)
[3] W.J. Stapor, “Single Event Effects (SEE) qualification”, IEEE NSREC Short Course, 1995
[4] JEDEC Standards, 2001
[5] G.I. Zebrev, I.A. Ladanov et al. “PRIVET – A Heavy Ion Induced Single Event Upset Rate Simulator in Space Environment”, RADECS 2005 Proceedings.
[6] V.S. Anashin, V.V. Emelyanov, G.I. Zebrev, I.O. Ishutin, N.V. Kuznetsov, B.Yu. Sharkov, Yu.A. Titarenko,
V.F. Batyaev, S.P. Borovlev “Accelerator Based Facility for Characterization of Single Event Upsets (SEU) and Latchups (SEL) in Digital Electronic Components”. A report at International Conference on Micro- and Nanoelectronics, October 2007, Zvenigorod, Russia
[7] D.L. Hansen et al. “Correlation of Prediction to On-Orbit SEU Performance for a Commercial 0.25-um CMOS
SRAM” IEEE Trans. on Nuclear Science, Vol. 54, No. 6, p.2525, Dec. 2007
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