IEEE Transactions on Nuclear Science, Vol. NS-3 1, No. 6, December 1984

MICRODOSIMETRIC ANALYSIS OF PROTON INDUCED REACTIONSIN SILICON AND GALLIUM ARSENIDE

G. E. FarrellPhysics Research Division

Emmanuel College400 The Fenway

Boston, Massachusetts 02115

P. J. McNulty and Wagih Abdel-KaderPhys ic s DepartmentClarkson University

Potsdam, New York 13676

ABSTRACT

Microdosimetric comparisions of volumes ofsilicon and gallium arsenide exposed to protons of 25to 300 MeV have been performed using a computersimulation. Significant differences between siliconand gallium arsenide are seen in the energy-depositionspectra. The effect of the surrounding material, the

energy and mass spectra of the recoiling nuclei, andthe effect of scaling are also presented and dis-cussed.

INTRODUCTION

Radiation-induced errors in microelectroniccircuits have in recent years been recognized as a

serious problem. Charged particles lose energy byionizing the medium through which they pass. leavingbehind a wake of electron-hole pairs. The sudden in-

troduction of this charge into a microelectronic de-vice can result in errors known as single-event upsets(SEU's). The energetic protons in the radiation belts

and in the cosmic rays can induce SEU's, eitherdirectly or through secondary particles from nuclear

reactions. The most important secondary particle em-

erging from a proton-induced nuclear reaction, at

least as far as SEUs are concerned, is the recoilingfragment of the target nucleus. The prediction andcontrol of these upsets is crucial to the functioningof satellite systems, and our ability to quantitative-ly model SEUs sufficient to accurately predict rateswill depend ultimately on the ability to model the de-

position of energy and the consequent generation ofcharges in microvolumes of given dimensions.

An SEU will occur if an ionizing particle de-posits more than a critical amount of charge withinone of the sensitive microscopic volume elements on a

device. We previously presented theoretical en-

ergy-deposition spectra generated in silicon bynuclear interactions initiated within the sensitivevolume (1-3). These calculations were compared to ex-

perimental data obtained using Ortec siliconsurface-barrier detectors, all with a cross sectional

2

area of 25 mm and thicknesses ranging from 2.5 to 97micrometers exposed to protons ranging in energy from25 MeV to 158 MeV. The agreement was quite good.

*

Work supported by Air Force Contracts No.F19628-82-K-0039 from the Air Force GeophysicsLaboratory and F19628-82-K-0004 from the Rome AirDevelopment Center.

In this paper we extend the calculations to

gallium arsenide and we include, for both Si and GaAs,the contributions from interactions that are initiatedoutside the sensitive volume. We find for bothmaterials that the contributions from interactions in-itiated in the surround are important for all but thehighest energy depositions.

COMPUTER MODEL

A Monte-Carlo type computer simulation was usedto model the nuclear reaction initiating the SEU. Thephysical assumptions upon which these codes are basedare similar to those of the codes developed byMetropolis et al. (4), Dostrovsky et al. (5), Bertini(6-9), and Guthrie (10,11). In our model, all thesecondary charged particles emerging from the nuclearevent are followed to determine how much, if any, en-

ergy is deposited in a sensitive volume of specifieddimensions. Then the total energy deposited is summedover all the secondaries emerging from each reactionto obtain the total energy deposited in the sensitivemicrovolume by ionization losses by the chargedsecondaries emerging from that event.

The small defined sensitive volume of silicon or

gallium arsenide corresponds to one sensitive regionon a microelectronics chip. The sensitive volume isembedded as shown in Fig. 1 in a larger volume whichrepresents the rest of the chip. In the simulationsdiscussed here, a unidirectional beam of protons of a

given incident energy is sent into the large volume.Some of these protons will pass through the sensitivevolume and deposit energy there, a small fraction willundergo nuclear reactions in the sensitive volume, andother protons will induce nuclear reactions elsewherein the larger volume. Both secondary particles and a

recoiling nuclear fragment result from these reactons

and some of these traverse the smaller sensitivevolume.

Fig. 1. Sensitive volume embedded in larger surround.

Model calculates the energy deposited within the

sensitive volume by charged particles emerging from

nuclear reactions initiated anywhere within the larger

volume.

0018-9499/84/1200-1073$1.001984 IEEE

1073

1074The paths of all of the charged secondaries arefollowed in the simulations to determine whether theycross the sensitive volume. A spectrum of the energydeposited in the sensitive volume per nuclear interac-tion is thereby obtained.

We previously reported that, according to oursimulation model, the energy-deposition spectra forthin slabs of silicon are dominated by contributionsfrom the nuclear recoil. This conclusion appears to betrue for large energy depositions in GaAs also. Itshould be noted that the model assumes the sensitivevolume to have the shape of a rectangular prism, whilethe detectors used in the experimental measurementsare cylindrical slabs. The difference does not appearto be significant.

RESULTS

Figures 2a and 2b compare the integral en-ergy-deposition spectra in one micrometer cubes ofsilicon and gallium arsenide. Figures 2c and 2d make asimilar comparison for 10 micrometer cubes. For bothsimulations the exposures were to unidirectional beamsof protons incident normal to the cube face with en-ergies of 25, 50, 100, 200 and 300 MeV. Thesecalculations include only inelastic nuclear reactionsinitiated inside the sensitive volume and do not in-clude contributions from reactions in the surround.Comparison shows that for the lower proton energiesconsiderably more energy is deposited in the siliconvolumes than the corresponding gallium-arsenide ones.For the 10 micrometer cube exposed to 25 MeV protonsthe number of events in which more than 2 MeV is de-posited is nearly 50 times larger in the silicon thanin the gallium arsenide. The explanation for this isin the nuclear kinematics. Gallium and arsenic aremore massive than silicon, and it is kinematicallymore difficult to give them as much recoil energy asto a silicon nucleus. The model also predicts thatsilicon reactions at these energies emit a sizableproportion of charged secondary particles while thesecondaries from gallium arsenide are mostly neutrons.

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2.dFig. 2. Integral energy-deposition spectra for protonsof different incident energies incident on a) a one

micrometer cube of silicon. b) a one micrometer cube

of GaAs, c) a 10 micrometer cube of silicon, and d) a

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At higher incident proton energies. especiallyfor smaller sensitive volumes, the long-range siliconnuclei leave the sensitive volume before depositingall of their energy. The gallium and arsenic recoils.being shorter, tend to remain inside and this leads togreater energy depositions in the smaller GaAs volumesthan in silicon volumes of the same dimensions. Thisis seen in comparing the corresponding curves in Figs2a and 2b. If the sensitive volume has largerdimensions a greater fraction of the silicon recoilremains inside and the energy depositions are largerfor Si than for GaAs as can be seen for 10 micrometersin Figs. 2c and 2d. Only for the highest energy de-positions in the 10 micrometer cubes do the GaAscurves equal the corresponding Si ones.

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1075One goal of our research effort is to determine

how the energy deposition in a sensitive volume scaleswith feature size. A simple approach to scaling is il-lustrated in Fig. 3 by plotting the ratio of the crosssection for some threshold energy deposition. E.D., ina cube of dimensions. t. to the volume of the cube asa function of incident proton kinetic energy for vari-ous values of E.D./t. Since the probability for in-elastic interactions per unit volume is uniform overthe range of sizes considered, the data for E.D./t > 0for all values of t lie on the same curve. One canthus obtain the cross section for a nuclear reactionin a microvolume of arbitrary area A and thickness tby multiplying the abscissa value by A t. Such simplescaling also appears to hold for small energy de-positions in small microvolumes but not for larger en-ergy depositions in thicker microvolumes. The datafor E.D./t > 1 MeV per cubic micron fall on the samecurve for smaller cubes but not for the largest. AsE.D./t increases the divergence for the larger cubesizes increases quickly.

Effects of Surround

A closer approach to real conditions in a chip ismade by embedding the small sensitive volume in alarger volume as in Fig. 1. For sufficiently smallsensitive volumes. most of the energy deposited willcome from interactions initiated outside of thesensitive volume. In Fig. 4a are shown the calculatedintegral energy-deposition spectra in silicon for acubic sensitive volume of one micron with no surround.and for the same volume embedded in a 2 micron cube, a4 micron cube. and an 8 micron cube- all of silicon.The corresponding curves for gallium arsenide areshown in Fig. 4b. The low energy depositions are dueto secondary particles, while nuclear recoils dominateat higher energy depositions. The gallium arsenidedata in Fig. 4b show little increase as the large cubeis increased from 2 microns to 8 microns. except atthe smallest energy depositions where the long rangesecondaries dominate.

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Fig. 3. Ratio of the cross section for depositing atleast some value. E.D., in a cube of a) silicon and b)GaAs for dimensions t on a side versus the energy ofthe incident proton for different values of E.D./t and

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In silicon, events generated far from the sensitivevolume contribute significantly, as seen in Fig. 4a.This is presumably due to the longer range of the re-coiling nuclear fragment following a nuclear reactionin silicon. If one is concerned with lower energy de-positions (for example, circuits sensitive to alphaparticles) then the effect of energetic chargedsecondaries is more important. In that case the con-tribution from reactions initiated within a fewhundred microns of the sensitive volume must be in-cluded.

Most of the large-energy-deposition events aredue to the traversal of the sensitive volume by therecoiling nuclear fragment. The fragment deposits allor most of its energy within a short distance and is,thereby, a source of large energy depositions.Figures 5a and 5b are calculated histograms of theatomic mass spectra of the nuclear fragments resultingfrom proton-induced nuclear reactions in silicon andgallium arsenide for an incident energy of 100 MeV.The energy spectra of the recoiling heavy fragmentsemerging from these reactions are plotted for siliconand gallium arsenide in Figs. 6a and 6b, respectively.The recoils in GaAs have lower energies and cor-respondingly shorter ranges than those in silicon; asa result, the stopping power or linear energy transfer(LET) of a recoil in GaAs is typically higher than fora recoil in silicon. If the smallest dimension of thesensitive volume is smaller than the range of thetypical recoil, the LET determines the energy de-posited in the sensitive volume and larger energieswill be deposited for the same dimensions in GaAs;if, on the other hand, the smallest dimension is larg-er than the range of the energetic recoils, the total

energy carried by the recoil determines the energy de-posited and larger energies will be deposited if thesensitive volume lies in silicon.

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SUMMARYTheoretical energy-deposition spectra from pro-

ton-induced nuclear reactions in microscopic volumesof silicon and gallium arsenide have been calculated.The computer model has previously been shown to givegood agreement with experimental values from silicon.Greater energy depositions are seen in silicon for lowincident proton energies and large sensitive volumes,while gallium-arsenide reactions deposit more energyat the higher incident proton energies in smallsensitive volumes. The effect of the surround isparticularly important with silicon, as the residualnuclei from silicon reactions can have long rangesbut, even in GaAs. the contribution from nuclear re-actions initiated outside the sensitive volume willexceed the contribution from those initiated withinfor circuits having LSI geometries.

7. H.W. Bertini, Phys. Rev. IU, 1261 (1968). 1077

8. H.W. Bertini, Phys. Rev. 18, 1711 (1969).

9. H.W. Bertini, Phys. Rev. U, 631 (1972).

10. M.P. Guthrie, ORNL-4379, Oak Ridge NationalLaboratory, Oak Ridge, Tennessee (1969).

11. M.P. Guthrie, ORNL-TM-3119. Oak Ridge NationalLaboratory, Oak Ridge, Tennessee (1970)

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Fig. 6. Distribution of the kinetic energy of the re-

coiling nuclear fragment following interactionsbetween 100 MeV protons and a) silicon nuclei or b)GaAs nuclei.

REFERENCES

1. P.J. McNulty, G.E. Farrell, and W.P. Tucker, IEEETrans. Nucl. Sci. NS-28. 4007 (1981).

2. G.E. Farrell and P.J. McNulty, IEEE Trans. Nucl.Sci. NS-29, 2012 ( 1982) .

3. S. El Teleaty, G.E. Farrell, and P.J. McNulty.IEEE Trans. Nucl. Sci. NS-30. 4394 (1983)

4. N. Metropolis, R. Bivins, M. Storm, A. Turkevich.J.M. Miller, and G. Friedlander, Phys. Rev. 110,185 (1958).

5. I. Dostrovsky, Z. Fraenkel. and G. Friedlander,Phys. Rev. 116, 683 (1960).

6 H.W. Bertini, Phys. Rev. 131. 1801 (1963).

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