Two parameter Bendel model calculations for predicting proton ...

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 37, NO. 6, DECEMBER 1990

1966

TWO PARAMETER BENDEL MODEL CALCULATIONS FOR PREDICTING PROTON INDUCED UPSET

W.J. Stapor, J.P. Meyers2,J.B. Langworthy, and E.L. Petersen Naval Research Laboratory Washington, D.C. 20375-5000 h3STRACT

data by expressing both parameters in terms of the threshold energy. Generalized curves from the one parameter formula are shown in Figure 1 for the upset cross section versus proton kinetic energy. These curves indicate a distinct threshold with a rapid rise up to constant value. Thus, the task of obtaining useable proton SEU rates in space was

The present best method of predicting proton induced SEU rates in the proton radiation belts is given by W.L. Bendel [1,2, and 31. It is a semi-empirical technique and describes the upset cross section as a function of a single experimental parameter. Bendel presented a two parameter approach in [3] but decided to emphasize the simpler one parameter approach since it could adequately describe the UPSETS per PROTON/cm^2 per BIT 1.OE-09 available data. Shimano et al. [4] presented results showing slight improvements in the fits using the two parameter Bendel model, and a slightly different two parameter model has been used by Normand [5]. Recent energy dependent 1.OE-13 experiments at this and other laboratories [6] on small 1.OE-14 feature size devices have produced data that is clearly not adequately fit by the single parameter approach. This paper 1.OE- 15 demonstrates that improved fits of both new and old data 1.OE-16 can be obtained with a two parameter approach. Shimano's 1.OE-17 work focussed on four devices, three of which are from older 1.OE-18 technologies with large feature sizes (> 1.5 pm) and are no L 1.OE- 1 9 10 100 1000 longer representative of the newer small feature sized (< 1.5 PROTON KINETIC ENERGY (MeV) pm) devices. This work provides summary analyses with the improved Bendel model on much of the existing published Fwre 1. Generalizedcurves from the single parameter Bendel model that proton data [S-131, and also on recent data [6,14, and 151 on describe the proton upset cross section as a function of proton energy. newer devices. I

I

1 1 ,

1

,

,

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,

reduced to measuring the upset cross section at only a few energies (usually only 1 energy given the great expense of The original Bendel approach came from the observation accelerator time) and then fitting the data to determine the that much of the proton SEU data as a function of incident A parameter and the overall SEU cross section energy proton kinetic energy followed a relationship resembling the dependence. With the energy dependence information for a proton nuclear reaction cross section in silicon. A formula given device, the proton SEU rate could be predicted from was developed that had two terms, one expressing the a convolution with a given proton environment in a given limiting cross section at infinity, "U(-)", and the other orbit. expressing the rapid rise of the cross section from the threshold energy, "A. Bendel recognized that the problem The single parameter model is practical and could be simplified while still adequately fitting the available accurate, only if the devices have a proton SEU energy dependence accurately described by the single parameter formula. We have made proton SEU energy dependence measurements on a new NMOS (with CMOS peripherals) Work Supported by ONT 6.2 Microelectronics RL34M42 and by device, the IDT 7164, at 5 energies from 30 MeV up to 149 the DNA Single Events Program MeV and have observed a deviation from the shape predicted from the single parameter Bendel formula. The Sachs Freeman Associates, Landover MD 20785 data, shown in Figure 2, do not have the rapid rise, from the

INTRODUCTION

0018-9499/90/ 1200-1966$01.OO O 1990 IEEE

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parameter Bendel model. The lower set of entries in Table 1 show these results. As A should always be lower than the lowest energy at which upsets are observed, the fits are not internally consistent. This problem arises because the single parameter not only fues the apparent low energy threshold for the data, but also the asymptotic value of the cross section. Also, as in the case of the 7164 device, there is a spread in the values of the best Bendel A parameter from 45 up to 60 when the data points are treated individually. This gives a large factor of approximately 300 in the ratio of highest to lowest upset rate prediction for the given orbit.

1 AND 2 PARAMETER BENDEL MODEL IDT 7164 1 OE-12

1.OE-14

UPSET CROSS SECTION (cmP/bit)

1

-

1.OE- 16 0

*

NRL DATA, HARVARD 1 PARAMETER

- 2 PARAMETER 20

40

I

I

I

I

60

80

100

120

140

160

ENERGY (MeV)

Figure2. Proton upset cross section versus energy for an IDT 7164. Indicated are 1 parameter Bendel curves for A=2553 and 30.00 MeV, with improved 2 parameter curve.

low energy point, to an asymptoticallyflat shape as described in Figure 1, but instead, the data show no sharp low energy threshold and rise slowly over the energy range. As a consequence of this experimental result, different Bendel A parameters obtained by fitting at each energy separately will produce variations in the predicted upset rate at a given orbit. (The orbit in this case is a 600 nmi, 63" inclination, solar minimum environment.)

The upset energy threshold for proton upsets depends on the maximum path length of the sensitive volume, just as does the LET threshold for heavy ions [ I .For devices with large feature size, the limiting proton cross section is determined primarily also by the maximum path length, so the single parameter Bendel approach works. As devices become smaller, the proton upset rate transitions to a situation where the upset rate depends primarily on the minimum dimension, as for cosmic rays. Therefore a correction to the limiting cross section term must be made in the Bendel approximation.

TWO PARAMETER BENDEL MODEL A N D DATA

FITTING The two parameter formula contains the parameter, B, in place of a constant 24 used previously [2], and is given by,

Table 1 gives the incident proton energy, the measured upset cross section, the corresponding Bendel A parameter, and the upset rate prediction for the particular orbit. At each energy, that is, treating the upset cross section as if it were the only data taken on the device, a different A where X is in units of lo-'' upsets per proton/cm' per bit parameter can be obtained which produces a spread in the and, predicted upset rate. Figure 2 shows the one parameter yz Bendel model fits for the data at the lowest energy point Y= (E - A ) (dashed line labeled A = 25.53) and the highest energy point (dashed l i e labeled 30.00). For this particular case the ratio of highest to lowest predicted upset rate is a factor of 10. Assuming that all the data is reliable, which A parameter with E in units of MeV. The two parameter approach gives should be used to describe the upset rate? It is not clear a better fit to the data for the proton SEU energy using only single energy upset cross sections when knowledge dependence. The form of this model differs slightly from the of the proton energy dependence is not available. Unless the one used in the work of Shimano et al. [4]. Their model used energy dependence is known or measured, the best estimate a single parameter, S, instead of the factor (B/A)'*. We have of the upset rate is this case can only be specified to within chosen the formalism of the original 1 parameter Bendel a factor of 10 using the single parameter model. The better approach. In principle, the two formulas are identical. The fit to the entire dataset shown in Figure 2 is given by an physical significance of(B/A)I4 (as well as the S term in the improved, two parameter Bendel model. Shimano et al. formalism) is the "limiting cross section" [2,3] or the fitted value of the cross section at infinite energy. The data of Pickel and coworkers on a new CMOS/SOS device also does not fit the one parameter approach. The A x' minimization curve fitting program [16] was cross sections increase, from the low energy point, much used to fit the data to the both the original one parameter slower with energy than would be predicted by the single

(T)

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Table 1. Proton upset rate predictions from single parameter Bendel model. Data are for the IDT 7164 8Kx8 NMOS static RAM and a 16K CMOS/SOS RAM [6].

ENERGY (MCV)

DEVICE

CROSS SEcllON

(an2/bit)

BENDKL. A (MCV)

only fits well in certain energy regions, and misses badly for newer, small feature sized devices. We have found these devices to have typical Bendel A values greater than approximately 17 MeV and measured asymptotic cross cm2/bit. sections less than 1 x

UPSEIspr BIT-DAY

RESULTSA N D DISCUSSION 1.18x10-14

CMOS/SOS

II

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38

0.95x1r18

45

1.0xldO

90

l.oOxl(rI8

SI

l.lxlo-l1

II

As already mentioned, we have re-evaluated the new data and some old data with an improved Bendel model using an additional free parameter, B, described in Equation (l), which allows for a variation in the asymptotic cross section from the single parameter dependence. Figures 3 through 15 show the measured cross sections and the fitted cross sections for the 1 and 2 parameter models as a function of proton kinetic energy. The figures show results for 13 devices, 10 older ones and 3 new ones. The older devices are; the Texas Instruments 4044, the National Semiconductor MM5280,the Intel C2107B, the Motorola MCM 4116AC-20, the Mostek MK 41165-2, the Signetics 8x350,and the Fairchild 93L422,93425,93425A, and 93422. The newer devices are; the Integrated Device Technology 7164 and 6116, and a Texas Instruments CMOS/SOS device.

and two parameter Bendel model. Data points in each dataset were treated with equal weight instead of using statistical weight factors. One reason for this treatment in the fitting procedure was to impose a more stringent constraint on the curve fit to try to match the lower energy Table 2 contains the resulting summary of the data values. Another reason is that the actual uncertainties, comparison between the one and two parameter models. both statistical and systematic, of the datasets are not Table 2 shows columns of the device name and device data actually known. It is suspected that the systematic reference, parameters for the single and double parameter uncertainties, which tend to affect the overall dataset model with the associated limiting cross sections, a goodness normalizations, are large compared to the statistical of fit parameter, and a predicted proton upset rate for an uncertainties anyway, so that the equal weighing will average arbitrary orbit. The goodness of fit parameter gives a out data from different laboratories on the same device. The measurement of how well the model fits the data. resulting fitted parameters were then used to create plots of both the one parameter fit and the two parameter fit with There are many ways to quantify how well a the data and are shown in Figures 3 through 15. function matches the data. We have chosen a goodness of fit The fitting of the datasets was no easy task since for some cases, the x2 minimization technique would attempt to produce values for the A parameters that would be larger than the lowest energy, resulting in attempts to take square roots of negative numbers in both models. In a few cases the lowest energy data point had to be ignored when fitting the data with the single parameter model. When it was included, the resulting curve would miss the rest of the data points as mentioned earlier in this text. The removal of the point yielded the single A parameter to be larger than the smallest energy value. Even though the lowest energy point was not included in the fit, the results were a single A parameter that better fit the rest of the data, even though the fit would totally miss the lowest energy point.

1.OE-12~

1.OE-13

=

1.OE-14

= II

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The advantage of the two parameter model is that it allows better fitting of the experimental data in the high

energy regions, while preserving the apparent low energy proton upset threshold. Although the single parameter model seems to follow the overall shape of the datasets, it

1.OE-16

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Figure 3. Proton upset cross section data versus energy for the TI 4044. One and two parameter Bendel curves are also indicated.

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MK41163-2

MM5280 1.E-11

UPSET CROSS SECTION (cmA2/bit)

UPSET CROSS SECTION (crn^2/bit)

1.E-11

I /

1.E-13

1 PARAMETER

2 PARAMETER

1.0E-13 0

20

40

60

80

100

120

140

ENERGY (MeV)

Figure 4. Proton upset cross section data versus energy for the National MUS280. One and two parameter Bendel c u m are indicated.

Figure 7. Proton

upset cross section data versus energy for the Mostek MK6114J-2. One and two parameter Bendel curves are also indicated.

8x350

C2107B UPSET CROSS SECTION (cmA2/bit)

1.OE-08

l.E-10

1.OE-10

l,OE-”i

I

,

,

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i”l

1 PARAMETER

- 2 PARAMETER

1

i

1.OE-11

1 .OE- 12

10-13

’

0

0

20

40

60

80

100

120

C2107B.One and two parameter Bendel curves are also indicated.

1 PARAMETER

2 PARAMETER

I ~

10

20

30

50

40

60

70

Figure% Proton upset cross section data versus energy for the Signetics 8x350. One and two parameter Bendel curves are also indicated.

93L422

MCM4116 AC20 1 .E- 10

DATA

ENERGY (MeV)

140

ENERGY (MeV) Figure 5. Proton upset cross section data versus energy for the Intel

*

UPSET CROSS SECTION (crn^2/bit) -L l.M-lok

UPSET CROSS SECTiON (crn-2Ibit)

___----

1 , s 1 1

l.E-12

, , , , ,,,, l.E-13

/#(, El] , ,,,,,

,

- 2 PARAMETER

* cI

DATA 1 PARAMETER

2 PARAMETER I I

10

100

1000

10000

ENERGY (MeV) Figure 6. Proton

upset cross section data versus energy for the Motorola MCM 6114AC-20. One and two parameter Bendel curves are also indicated.

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93425

6116

UPSET CROSS SECTION (crna2/bit)

1.OE-09

L

1.OE- 1 0

UPSET CROSS SECTION (cmA2/bit)

I

1.OE - 1 2

/

1.OE - 1 3

II

I

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---

1 PARAMETER

- 2 PARAMETER

I

10

100

1000

l.E-16r

0

ENERGY (MeV)

I I

' 20

10

30

40

60

Bo

70

80

ENERGY (MeV)

Figure 10. Proton upset cross section data versus energy for the Fairchild 93425. One and two parameter Bendel curves are also indicated.

1.OE- 1 0

Figure U.Proton upset cross section data versus energy for the IDT 6116. One and two parameter Bendel curves are also indicated.

I

1.OE-11-

0

50

ENERGY 1 0 0 (MeV)

150

200

Figure 14. Proton upset cross section data versus energy for the IDT 7164.One and two parameter bendel curves are also indicated.

CMOS

93422 UPSET CROSS SECTION (cm-Z/bit)

1.M-1OE

I

UPSET CROSS SECTION (crnWbit)

1.OE-14

*

1.OE- 16

DATA 1 PARAMETER

2 PARAMETER

1.OE- 17 1.OE-13:

, I I

2 PARAMETER

1.OE- 1 8

>

0

50

100

160

200

250

ENERGY (MeV)

Figure U.Proton upset cross section data versus energy for the Fairchild 93422. One and two parameter Bendel curves are also indicated.

Figure 15. Proton upset cross section data versus energy for a Texas Instruments WOS/SOS device [6]. One and two parameter Bendel curves are also indicated.

-7- 1 - -

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parameter which is the calculated average percentage error or deviation between the data and the fitted curve. (See the equation at the bottom of Table 2). Small values for this goodness of fit parameter indicate that the fitted function, on the average, nearly matches the data. If this goodness of fit is equal to zero, the function exactly fits all of the data. Large values of this fit parameter are indicative of a large average deviation between data and fitted function. In all cases except one, the goodness of the fits for the 2 parameter Bendel model are better overall which necessarily leads to more accurate proton upset rate predictions. The important issue is how different are the proton upset rate predictions based on the model comparisons. This effect on the rate predictions is summarized in Figure 16. This figure shows the ratio of the

Figure 13 shows a low A value (A = 17.81) fit and the improved fit with the data for the 6116 device. This would be the assumed energy dependence of the data if no other data were available. The resulting upset rate calculation is 469 times the two parameter model which incorporates the actual measured energy dependence.

CONCLUSIONS

DEVICE 4044 MM5280 C2107B MCM4116 AC-20 1 MK4116 J-2 8x350 93L422 93425 93425A 93422 0 001 6116 (A.17.81) 7 iaai-oe 6116 (A-26.57) I OIOI 7164 (A=25.53) 7164 [A=29.85) 0 001 CMOS/SOS

data, as indicated in Figures 2 and 14. In Figure 2, both low and high values for A are plotted with the data for the 7164 device. In Figure 14, another high energy A value is plotted with the 7164 data. This observation leads to the idea that most of the upset rate depends on the high energy data (> 50 MeV), at least for the selected orbit. But when high energy data is not available, and the one parameter approach is used, there will be large uncertainty in the predicted upset rate.

,088

0 020 1 ,E8

173, 1 I*, 1 OS3 I

*eo

0 760

,288

0

oes

Figure 16. Bar chart of ratios of upset rate predictions from 2 parameter model over 1 parameter model for devices in this study. A ratio of one indicates the same upset rate prediction.

upset rate predictions from the two parameter to the one parameter Bendel model. Ratios of 1.0 indicate the same upset rate prediction resulting from the models. It is readily seen that all the older devices have ratios near 1.0, the lowest ratio in this set being 0.759 and the highest 1.731. The close ratios indicate that the differences between the two models are not substantial, at least for these devices with large feature sizes. The situation is not the same for the newer, small feature sized devices. Indicated ratios for these devices are all less than 1.0, and much less than 1.0 in four out of five cases shown. The upset rates predicted by the improved approach are lower. We have indicated the ratios for both the 7164 and the 6116 devices using suitable low and high Bendel A values for each device to compare the upset rate predictions with the well fitted 2 parameter model. The resulting ratios as well as the goodness of fit indicate that the larger Bendel A parameters more nearly match the two parameter rate predictions. The larger Bendel A values tend to fit the high energy data but badly misses the low energy

The two parameter Bendel model, represents an improvement over the existing single parameter model in terms of the goodness of fit to actual proton upset data. It especially gives a better fit to the data from devices with small feature dimensions, which ultimately leads to a more accurate proton error rate prediction. Small feature sized devices have proton upset energy dependence that cannot be accurately described with the one parameter model and only one data point. Large errors (possibly orders of magnitude) can result in upset rate predictions due to these inadequacies. It is important to know or measure the proton upset rate for a few energies, from near threshold up to approximately 150 MeV. There are no substantial differences in proton error rate predictions from one and two parameter approaches for older devices with larger feature sizes.

REFERENCES W.L. Bendel and E.L. Petersen, "Proton Upsets in Orbit," IEEE Trans. Nucl. Sci., NS-30, 4481 (1983). W.L. Bendel, "Proton-Induced Single Event Upsets in 71 Earth-Satellite Environments," NRL Report 5364,1984. W.L. Bendel and E.L. Petersen, "Predicting Single Event Upsets in the Earth's Proton Belts," IEEE Trans. Nucl. Sci., NS-31, 1201 (1984). Y.Shimano, T. Goka, S.Kuboyama, K. Kawachi, T.Kan&, and Y. Takami, "The Measurement and Prediction of Proton Upset," IEEE Trans. Nucl. Sci., NS-36, 2344 (1989).

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E. Normand and WJ. Stapor, submitted for publication, 1990IEEE Trans. Nucl. Sci., December issue. This work used a two parameter approach of Stapor that was presented but unpublished in 1989.

J.C. Pickel, B. Lawton, A.C. Freedman, and PJ. McNulty, "Proton Induced SEU in CMOS/SOS," Journal of Radiation Effects Research and Engineering, Vol. 7, #1, pg 69, 1989. E.L. Petersen, J.B. Langworthy, and S.E. Diehl, "Suggested Single Event Upset Figure of Merit," IEEE Trans. Nucl. Sci., NS-30,4533 (1983). R.C. Wyatt, et al., "Soft Errors Induced by Energetic Protons," IEEE Trans. Nucl. Sci., NS-26, 4905 (1979). PJ. McNulty, et al., "Upset Phenomena Induced by Energetic Protons and Electrons," IEEE Trans. Nucl. Sci., NS-27, 1516 (1980). C.S. Guenzer, EA. Wolicki, and R.G. Allas, "Single Event Upset of Dynamic RAMs by Neutrons and Protons," IEEE Trans. Nucl. Sci., NS-26, 5048 (1979). C.S. Guenzer, et al., "Single Event Upsets in RAMs Induced by Protons at 4.2 GeV and Protons and Neutrons Below 100 MeV," IEEE Trans. Nucl. Sci., NS-27, 1516 (1980). D.K. Nichols, W.E. Price, and CJ. Malone, "Single Event Upset (SEU) of Semiconductor Devices -- A Summary of JPL Test Data," IEEE Trans. Nucl. Sci., NS-30, 4520 (1983).

D.K. Nichols, W.E. Price, and J.L. Andrews, "The Dependence of Single Event Upset on Proton Energy (15 - 590 MeV)," IEEE Trans. Nucl. Sci., NS-29, 2081 (1982). NRL Data, Unpublished, UC Davis 1990. NRL Data, Unpublished, UC Davis 1990, Harvard 1988. 1161

NRL program SLOPEFINDR, WJ. Stapor, P.T. McDonald, and J. Cummings, (1986).

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