6
IEEE Ttanactions on fuctea-t Science, t'oZ.NS-22, No.6, Vecembea 1975 SATELLITE ANOMALIES FROM GALACTIC COSMIC RAYS D. Binder, E. C. Smith, and A. B. Holman Hughes Aircraft Company Culver City, California 90230 Abstract 500 20 kf Anomalies in communication satellite operation 014 have been caused by the unexpected triggering of 215 digital circuits. Interactions with galactic cosmic i 0 rays were investigated as a mechanism for a number of Hi O these events. The mechanism assumed was the charging 12 of the base-emitter capacitance of sensitive tran- sistors to the turn-on voltage. The calculation of PRESET Hi the cosmic ray event rate required the determination HOkI 40k! of transistor parameters, charge collection efficiencies, and the number of sensitive transistors. The sensitive transistors were determined by K H3 analyzing the results of a scanning electron micro- HQ3 scope experiment. Calculations with iron cosmic rays 20kil < resulted in an event rate of 3.1 x 10-3 per transistor per year, in reasonable agreement with the observed rate of 1.5 x lo-3. Introduction Anomalies in communication satellite operation have been caused by the unexpected triggering of digital circuits. Although the majority of these events have been attributed to charge buildup from (1,2) high temperature plasmas, some of the events appear to be caused by another mechanism. The pur- pose of this paper is to investigate interactions with galactic cosmic rays as an additional mechanism. The satellite anomalies studied were caused by the triggering of flip-flop circuits. The particular mechanism assumed for the cosmic ray interaction was the charging of the base-emitter capacitance of critical transistors to the turn-on voltage. The charge is produced by the dense ionization track of an energetic, high-Z cosmic ray. The following sections describe the determination of the number of sensitive transistors, the charge collection efficiency, the transistor parameters, and the energy spectrum of the penetrating cosmic rays. All these quantities were required as input data for a computer code called CRAC, developed for this problem. The code was used to calculate the solid angle in which cosmic rays supplied sufficient energy to turn on the transistors. The theoretical event rate was then calculated and compared with satellite data. Circuit Effects The circuits responsible for the anomalies are JK flip-flops, and the schematic is shown in Figure 1. The analysis of the cosmic ray triggering rate requires the identification of sensitive transistors in the flip-flop circuit. A scanning electron microscope (SEM) was used for this purpose. This technique was not meant as an exact simulation of the cosmic ray event, but was intended to locate the sensitive tran- sistors which could cause the change of state of the flip-flop. The SEM electron beam creates dense ioni- zation at depths in the integrated circuit chip which Figure 1. J-K Flip-Flop Circuit with Transistor States correspond to the junction boundaries of the tran- sistors. The ionization is confined to an area with ,2 micron diameter which approximately simulates the cosmic ray track. In addition, the well-defined SEM beam allows the irradiation of individual transistors and, indeed, separate junctions on each transistor. Proper identification of sensitive transistors, once located, was assured by taking a complete set of SEM photographs for comparison to chip fabrication drawings. The SEM has the capability of producing electrons of 2 to 30 KeV in energy with beam currents from the picoampere to the microampere intensity range. For beam penetration to the sensitive transistor junctions in the chip, a 30 KeV beam was required. Scans of the chip transistors with beam currents up to a few hundred nanoamperes were utilized during the experiments. Electron transport Monte Carlo calculations were performed to obtain profiles of electron energy depositions at various depths in the chip. These energy depositions then correlate directly to the density of ionization created by the incident electron beam. The BETA II computer code (3) was used for these Monte Carlo calculations. Approximately 1000 electron histories were followed at normal incidence to a 0.75 micron Si°2 passivation layer backed by silicon. "Detectors" at various depths were set up to measure the electron energy depositions. The results for a 30 KeV incident beam are found in Figure 2. Note that the energy deposition, and therefore the ionization density, peaks in the vicinity of the emitter-base and base-collector junctions, at an approximate depth of two microns into the chip. This was the basis for requiring a SEM energy of 30 KeV for the experiment. An external circuit shown in Figure 3 was used during the irradiations to monitor the state of the flip-flop. Changes of state were identified by means 2675

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Page 1: Satellite Anomalies from Galactic Cosmic Rays

IEEE Ttanactions on fuctea-t Science, t'oZ.NS-22, No.6, Vecembea 1975

SATELLITE ANOMALIES FROM GALACTIC COSMIC RAYS

D. Binder, E. C. Smith, and A. B. HolmanHughes Aircraft Company

Culver City, California 90230

Abstract500 20 kf

Anomalies in communication satellite operation 014have been caused by the unexpected triggering of 215digital circuits. Interactions with galactic cosmic i 0rays were investigated as a mechanism for a number of Hi Othese events. The mechanism assumed was the charging 12of the base-emitter capacitance of sensitive tran-sistors to the turn-on voltage. The calculation of PRESETHithe cosmic ray event rate required the determination HOkI40k!of transistor parameters, charge collectionefficiencies, and the number of sensitive transistors.The sensitive transistors were determined by K H3analyzing the results of a scanning electron micro- HQ3scope experiment. Calculations with iron cosmic rays 20kil <resulted in an event rate of 3.1 x 10-3 per transistorper year, in reasonable agreement with the observedrate of 1.5 x lo-3.

Introduction

Anomalies in communication satellite operationhave been caused by the unexpected triggering ofdigital circuits. Although the majority of theseevents have been attributed to charge buildup from

(1,2)high temperature plasmas, some of the eventsappear to be caused by another mechanism. The pur-pose of this paper is to investigate interactions withgalactic cosmic rays as an additional mechanism.

The satellite anomalies studied were caused bythe triggering of flip-flop circuits. The particularmechanism assumed for the cosmic ray interaction wasthe charging of the base-emitter capacitance ofcritical transistors to the turn-on voltage. Thecharge is produced by the dense ionization track of anenergetic, high-Z cosmic ray.

The following sections describe the determinationof the number of sensitive transistors, the chargecollection efficiency, the transistor parameters, andthe energy spectrum of the penetrating cosmic rays.All these quantities were required as input data for acomputer code called CRAC, developed for this problem.The code was used to calculate the solid angle inwhich cosmic rays supplied sufficient energy to turnon the transistors. The theoretical event rate wasthen calculated and compared with satellite data.

Circuit Effects

The circuits responsible for the anomalies are JKflip-flops, and the schematic is shown in Figure 1.The analysis of the cosmic ray triggering rate requiresthe identification of sensitive transistors in theflip-flop circuit. A scanning electron microscope(SEM) was used for this purpose. This technique wasnot meant as an exact simulation of the cosmic rayevent, but was intended to locate the sensitive tran-sistors which could cause the change of state of theflip-flop. The SEM electron beam creates dense ioni-zation at depths in the integrated circuit chip which

Figure 1. J-K Flip-Flop Circuit with Transistor States

correspond to the junction boundaries of the tran-sistors. The ionization is confined to an area with,2 micron diameter which approximately simulates thecosmic ray track. In addition, the well-defined SEMbeam allows the irradiation of individual transistorsand, indeed, separate junctions on each transistor.Proper identification of sensitive transistors, oncelocated, was assured by taking a complete set of SEMphotographs for comparison to chip fabricationdrawings.

The SEM has the capability of producing electronsof 2 to 30 KeV in energy with beam currents from thepicoampere to the microampere intensity range. Forbeam penetration to the sensitive transistor junctionsin the chip, a 30 KeV beam was required. Scans ofthe chip transistors with beam currents up to a fewhundred nanoamperes were utilized during theexperiments.

Electron transport Monte Carlo calculations wereperformed to obtain profiles of electron energydepositions at various depths in the chip. Theseenergy depositions then correlate directly to thedensity of ionization created by the incident electronbeam. The BETA II computer code (3) was used for theseMonte Carlo calculations. Approximately 1000 electronhistories were followed at normal incidence to a0.75 micron Si°2 passivation layer backed by silicon."Detectors" at various depths were set up to measurethe electron energy depositions. The results for a30 KeV incident beam are found in Figure 2.Note that the energy deposition, and therefore theionization density, peaks in the vicinity of theemitter-base and base-collector junctions, at anapproximate depth of two microns into the chip. Thiswas the basis for requiring a SEM energy of 30 KeV forthe experiment.

An external circuit shown in Figure 3 was usedduring the irradiations to monitor the state of theflip-flop. Changes of state were identified by means

2675

Page 2: Satellite Anomalies from Galactic Cosmic Rays

..

I .,I' -4SI\

in

Z F- <

"I~~~~~~~~~~~~~~~~COLLECTOR -.-- SUBSTRATE

\\

\_

x0

2 4 6 8

DEPTH, MICRONS

Figure 2. Deposition Profile of 30 KeVScanning Electron Microscope Beam

U

Transistors Q2 and Q3, when irradiated by the SEMat the collector-base junction, caused a change ofstate at about 18 nA of beam current. Turning Q2 orQ3 ON causes Q4 to go ON and Q6 OFF. In addition, thecollector voltage of Q3 drops to about 0.8 volts, whichdrops one emitter voltage of Q8 from "HI" to "LO,"causing the collector current to decrease to zero. Thecollector current of Q8 supplies the base current ofQ10, which also goes to zero, turning Q10 OFF. WithQIO OFF, Q9 turns OFF and Q7 turns ON. Since Q6 isOFF and Q7 is ON, the LO and HI inputs to the slaveflip-flop are reversed, turning Q18 and Q20 OFF,making Q high and Q low.

10The circuit was less sensitive

The same change of state was causedcollector-base of Q4, but at a beaminstead of 18 nA. The cause of thenot clear since turning Q4 ON turnsother transistor should be affected.

to Q4 than Q2 or Q3.by irradiating thecurrent of 30 nA,change of state isQ6 OFF, but no

Figure 3. External Circuit to MonitorFlip-Flop States

of two light bulbs in the external circuit. Initially,complete scans of the entire flip-flop chip were madeto determine the threshold beam intensity required tocause triggers. Generally, 1000 line scans of a fewmiliseconds duration per line were used to assureadequate coverage of each chip transistor. Typicalchip dimensions were approximately 1000 microns x1000 microns with individual transistors having lineardimensions of 20 to 100 microns.

With the 30 KeV beam, the SEM deposited about17 KeV in sensitive areas near p-n junctions. At thisenergy, each energetic electron produces 5000 hole-electron pairs. At a beam current of 10 nA, thecurrent collected at a junction (AICBO) is 5000 x

10 nA = 50 PA. Due to the high impedances in thecircuit, this current is sufficient to turn almost allOFF transistors ON and possibly initiate a change ofstate of the JK flip-flop. In Figure 1, the flip-flop is shown in one state, with most of thetransistors labeled ON or OFF. A description of theresults of SEM irradiations of specific transistorsis given below.

Q7Irradiating the collector-base junction of Q7

caused no change of state at beam currents as high as80 nA. Turning Q7 ON does not appreciably affect otherportions of the master flip-flop. The only directconnection is to Q9, which is already ON. In the slavecircuit, Q17 is affected by lowering one of the emittervoltages. Since an emitter of Q16 is also held low byQ6, we have an ambiguous state. With the SEM beamcontinuously on the collector-base of Q7, it wasdifficult to change states by pulsing the clock. Thisdifficulty would not arise with cosmic rays, since thecharge created decays rapidly compared to the timebetween cl ock pul ses.

Q13, Q15

In the slave portion of the circuit, irradiatingthe collector-base junctions of Q13 and Q15 caused achange of state. Turning Q13 ON directly, or turningQ15 ON which would turn Q13 ON, causes Q to go low,stopping collector current through Q17. The basecurrent_of Q18 is turned OFF, turning Q20 OFF andmaking high. The SEM beam currents for these changesof state were between 20 and 50 nA. Irradiating Q19(originally OFF) at beam currents up to 50 nA causedno change of state. The only possible effect ofturning Q19 ON would be to add to the collector currentof Q20, which is already ON.

In summary, changes of state were observed byirradiating the collector-base junctions of Q2, Q3, Q4,Q13 and Q15. Since the effect of Q4 is not understood,only four transistors were counted in calculating thesensitive area of the flip-flop.

Basic Mechanism

The cosmic ray supplies an instantaneous charge,part of which is collected across the various capa-citances of the transistor. The particular mechanismassumed for turning the transistor on was the chargingof the base-emitter capacitance to the turn-on voltage.A collection efficiency of unity was assumed in thebase and in the depletion region of the collector. Thefraction of the charge collected in the diffusionregion was estimated in the following way.

The cosmic ray track is a source of charge atvarious distances from the depletion zone. Assume that

2676

zuiaz0

Nz0

-JII

10

5

1 r,

Com

Page 3: Satellite Anomalies from Galactic Cosmic Rays

the collection efficiency is only a function of thedistance to that zone. Thus, the charge at each pointin the track has a unique probability for reaching thedepletion region. Since the depletion zone forms aninfinite sink beyond a plane boundary, we need tocalculate the probability of a point source of chargereaching that plane.

Diffusion from a point at the origin obeys therelation

n = (4¶Dt) 3/2e - (x + y2 + z2)/4Dt

where ICs is the saturated collector current, and IBis the base current. In the SN54L00, IB for the out-put transistor is 240 vA. The load ICs was variedfrom 210 ,uA to 840 pA, and ts varied from 7 ns to4.5 ns. The above relation was used to determine Tat assumed values of hFE from 20 to 40. In thisrange, the resulting value of T was 2.2 ns,indepenwdent of hFE. The corresponding value of thediffusion length L is 1.7 microns.

where n is the concentration normalized to unity andD is the diffusion constant. The fraction crossing aplane at a distance zo from the point is

t0 00

f(t) = f foo0 o0

f n dx dy dzzo

or

f (t) = 0. 5 [1 - erf (zo/V4E)1.

The concentration of the carriers that have notcrossed the boundary varies as e t/T, where T is theminority carrier lifetime. The fraction crossing theboundary in a time interval At is approximately

Af = e-t/T[f(t + At) - f(t)]

where t t + At/2. A step calculation was performed,summing the contributions in each time interval At,which was made small relative to T.

The results of the calculation showed that thefraction collected was approximately

f (zo) = 0. 5 e-zo/L

where L = SYT. Since the calculation assumed norecombination within the track, f(zo) is an upperbound on the collection efficiency of the diffusionregion.

Transistor Parameters

The transistor base width (0.8 micron) wasobtained from the manufacturer, 4) who also definedthe base material as 250 ohms/per square and thecollector as one ohm cm, gold-doped. From this data,using the Lawrence and Warner curves for gradedjunctions,(5) the depletion depth was 1.2 microns at5 volts. The emitter-base capacitance of 1.4 pf wasestimated from the observed emitter area of 1.5 x10-6 cm2, the above data, and the calculation shownin Warner and Fordemwalt's text.(6) The diffusionlength L was determined from the minority carrierlifetime and the diffusion constant in the relationL = SDY. An estimate of T was made by storage timemeasurements at the output of the SN54L00 gate. Thisgate is in the same series as the flip-flop, and theassumption was made that the fabrication procedurewas identical. The storage time of a transistorvaries with the lifetime according to the relation

Cosmic Ray

For a turn-on voltage of 0.6 volts, 0.8 pico-coulombs is required to charge the emitter-basejunction. Assuming an efficiency of one for themoment, 19 MeV must be deposited by the cosmic rayalong a track length of a few microns. In addition,the cosmic ray must penetrate the typical satelliteshielding which is on the order of 150 mils ofaluminum. These two requirements restrict the cosmicray particle to atomic numbers about 26, and GeVenergies. The requirements are satisfied by galacticcosmic rays in the iron group.

Galactic cosmic rays are predominantly protons,with small populations of heavier partic es. Measure-ments of the spectra of various nuclei (7, of galacticcosmic rays are shown in Figure 4. There is a markedsimilarity of the spectra of heavier elements to that

101

xJ

-j

0

z20LLJ-J

I Ei Z

UJ0

z

C,)

1 0-7 _ . \1-2 iol- 100 101 102 103

ENERGY (BeV/NUCLEON)

erfvt5/T = 1 - ICS/hFEIB Figure 4. Galactic Cosmic Ray Spectra. The Spectraare Functions of Solar Activity.

2677

Page 4: Satellite Anomalies from Galactic Cosmic Rays

of alpha particles. Below z1 GeV per nucleon (X56 GeV 103for iron) the spectra are strongly influenced by solaractivity, the lowest intensity corresponding to thehighest activity. Since the detector events occurredduring a solar activity minimum, the higher curves arerelevant to the analysis.

The variation in cosmic ray intensity with atomic \_\number is illustrated in detail in Figure 5. Note 102\that there is a peak around iron, followed by a sharpdecrease. The alpha particle spectrum used in our Aaanalysis is the uppermost helium curve of Figure 4.The iron spectrum was assumed to have the same shape,a valid approximation in the energy range of interest. a

7oC+N+OTo relate the absolute intensities, the data of u 10

Figure 6 were used.(8-13) The integrated intensity of \\alpha particles was assumed to be 300 times that of \\nuclei around iron. Note again the similarity in ?spectra. The spectral shapes are different after openetration through spacecraft materials, as discussed -_later in this section. < -.Mg+AI+Si

1.0As noted previously, the deposition of large

amounts of energy in small geometric dimensions A

requires heavy nuclei. The heavier nuclei deposit xenergy very quickly, when compared to the protons or Jalpha particles. The dense tracks of ionization are

U.

a few microns in diameter. The increased stopping Fe+Co4Nipowers for highly charged particles is shown in thedata of Northcliffe and Schilling(14) plotted in .1Figure 7 for protons, alpha particles, C12 and Fe56nuclei. Figure 8 shows the range-energy curves for thesame particles. The high energy-ends of the curves forcarbon and iron are taken from an extrapolation of

1o3 l l ~~~~~~~~~~~~~~~~~~~.01\\l 10 102 103 104

l | ENERGY, MeV/NUCLEON

Ic Figure 6. Integral Cosmic Ray Spectra.

o2 li-- io_11'"

CO IRON 1 Iz Ia

1 _'I~~~~~~~~~~~~~~~~~~~~~

V a

IIl~~ ~ Fiur 7. StppA Poe1rVaiu11~ ~ ~ Nuc ei i 1uinm

102

V 1 ~~~ ~ ~ ~ ~~0.1110 io2 io1i1 -1--- ~~~~~~~~~~~~~~~~~~RANGE(MILS ALUMINUM)

I ~~~~~~Figure 7. Stopping Power for VariousI ~~~~~~~~~Nucleiin Aluminum.

l'A l ;| | the proton ranges, using the standard A/Z relationship

0. 1 _ _ _ _ 'for particles of the same velocity.5 10 15 20 25 30 35 Cosmic ray radiation incident on a spacecraft must,

ATOMICNUMBER in general, pass through a moderate amount of materialbefore reaching the detector diode. The amount of

Figure 5. Relative Intensity of Cosmic Rays Versus shielding is different for every case, but it wasAtomic Number possible to construct a model for spacecraft shielding

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Page 5: Satellite Anomalies from Galactic Cosmic Rays

100

cq,

E8

8E

LL1

10

0.1 10 100

ENERGY PER NUCLEON (MeV/AMU)

0-u-JDQ

s10C)0

CVwu

10,000 4

Figure 8. Range-Energy Curves for VariousNuclei in Aluminum.

that approximates a number of typical cases. The modelwas constructed by using the outputs for variousspacecraft programs from a computer code, MEVDP, (15)used in spacecraft shielding studies. The codebasically works as follows. All major spacecraftstructure and shield materials are modeled in acomputer coded format. This includes solar arrays,coverglasses and substrates, thermal blankets andshields, antennae, equipment shelves, electronicboxes and primary components. A target point; e.g.,an integrated circuit chip, is chosen, and approximately1000 rays sent out in all directions so that each viewsan equivalent solid angle. Each ray scores the thick-ness of each structure and shield material it traversesand totals the thicknesses for that given direction.The totals are then compiled to yield a sphericalshell mass distribution about the target point ofinterest.

The various spacecraft materials were converted toan equivalent aluminum thickness for the purpose ofthis approximation. Compilations of mass distributionssurrounding various points throughout the spacecraftwere studied (electronics boxes and componentsincluded). A typical mass distribution for anelectronic component of interest is presented in thetable below. The equivalent aluminum thicknessesgiven are for all materials between the silicon chipand the exterior surfaces of the spacecraft.

TYPICAL SPACECRAFT MASS DISTRIBUTION

x

-J

zw

III~~~~~~~~~~~~~~~~~~~~~~~~~~~~

u. _ o Fe+Co+Ni10r-6 7

10-7 ~ X '~200 400 600' 800 1000 1200 1400

ENERGY PER NUCLEON (MeV/AMU)

Figure 9. Effect of Satellite Shieldingon Cosmic Ray Spectra

of such high energies pass through the spacecraft witha negligible change in spectrum. On the other hand,the modifications for the heavier nuclei can be signifi-cant, especially at the lower energy ends of thespectra.

Cosmic Ray Event Rate

The cosmic ray event rate per unit area of thetransistor base is determined by the integral

Equivalent AluminumShield Thickness (mils)

0 - 2020 - 5050- 100

100 - 150150 - 250250 - 400400 - 700700 - 12001200- 2000

.2000

Percent of 4r SteradiansEnclosed by GivenShi el d Thi ckness

00.11.02.010.015.020.030.020.0<2.0

The use of the differential cosmic ray spectra inconjunction with the range-energy curves and the massdistribution allows the calculation of the modifica-tion of the spectral shape and flux intensities afterpassage through the spacecraft to the silicon chip.Figure 9 presents the results of these calculations foralpha particles, C-N-0, and Fe-Co-Ni nuclei. Protons

v - (l/41TJ4d(E)dE f2f 2 cos e sin 6 de dp

¢1 01

where v is the event rate per unit area and f(E) is theisotropic incident flux. The limits of integration fore and + correspond to the ranges of angles where thecosmic ray deposits sufficient energy to turn thetransistor on. The transistor was approximated asa thin disc with a radius of 22 microns, and theevent rate was integrated over the surface area ofthe disc. In general, the limits of integration foro are functions of ¢, E and the radial position on thedisc. This feature makes the computation tedious andrequires the use of a computer program.

A computer program called CRAC (Cosmic Ray AnomalyCalculation) was previously developed for a similar

problem. (16) For the present problem, the followinginput data were used:

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1

Page 6: Satellite Anomalies from Galactic Cosmic Rays

¢(E) = 2.1 x 105cm2 sec-IGeVldE/dx = 26.7 E- 584 GeV/cm(Si)

Emin = 19 MeV

Emin is the minimum energy deposition for a chargecollection efficiency of unity. In the diffusionregion, the effective energy deposited varies as

.5(dE/dx)e-ZO/L. The computational time was minimizedby the use of a binary search for the limits ofintegration of o. This technique is useful whenthe range of integration is continuous. In that case,a binary search of n will yield an accuracy of onepart in 2n.

The results of the computation are shown inFigure 10. The event rate per transistor R is plotted

10

W= 3p

w 5

0 1 2

L (MICRONS)

Figure 10. Event Rate per Transistorof Diffusion Length L andWidth W.

The observed rate for the satellite was computedin the following manner. There were four eventsobserved during magnetically quiet times and for localtimes not normally associated with charging phenomena.These four events occurred during 17 satellite yearsof operation. It was estimated that 40 flip-flopscould cause the events.(17) As discussed previously,there were four sensitive transistors per flip-flop.On this basis, the observed rate was 1.5 x 10-3 pertransistor per year. This rate agrees reasonably wellwith the calculated value of 3 x 10-3, considering allthe uncertainties.

References

1. R. W. Fredericks and F. L. Scarf, TRW ReportNo. 09670-7021-RO-OO, August 1972.

2. D. A. McPherson, D. P. Cauffman, W. Schober, AIMPaper No. 75-92, Pasadena, January 1975.

3. T. M. Jordan, "Beta II," ART Research Corp.Report No. ART-60, October 1971.

4. G. Hass, private conmmuni-cation.

5. R. M. Warner, J. N. Fordemwalt, et al.,"Integrated Circuits," McGraw Hill, 1965,pp 90-92.

6.

7.

Ibid, P. 182.

P. Meyer, R. Ramaty and W. R. Weber, PhysicsToday 27 (No. 10), 23 1974.

8. W. N. Ness, Introduction to Space Science,(Gordon and Breach, 1965) Chapter 10.

9. W. R. Weber, Proc. 13th International CosmicRay Conference, Denver, (1973) p. 3568.

NASA Report, TM-X-53865, Section 2.3.1.

M. 0. Burrell and J. J. Wright, "The Estimationof Galactic Cosmic Ray Penetration and Dose Rates,"NASA TN D-6600, March 1972.

12. G. M. Comstock, C. Y. Fan, and J. A. Simpson, TheAstrophysical Journal, 155, 609 (1969).

13. G. M. Comstock, C. Y. Fan, and J. A. Simpson, TheAstrophysical Journal, 146, 51 (1966).

14. L. C. Northcliffe and R. F. Schilling, NuclearData A7, (Academic Press, 1970).

15. B. Liley and S. C. Hamilton, "MEVDP," AFWL-TR-69-68, 1969.

16. D. Binder, A. B. Holman, and E. C. Smith, HughesReport Number P74-485, November 1974.

17. K. R. Obert, private communication.

10.

11.

3 4

as a FunctionDepletion

as a function of W and L, where W is the base widthplus depletion depth and L is the diffusion length.The calculated value for the estimated transistor para-meters (W = 2-p and L = 1.7up) is 3.1 x 10 3events pertransistor per year. A large uncertainty is involvedin the effect of L, which was computed assuming onlybulk recombination. The effect of recombination with-in the track may reduce the effect of L, possiblycorresponding to the rate of L = 0. The accuracy ofthe computation is thus no better than a factor of 2.

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