IEEE Transactions on Nuclear Science, Vol. NS-30, No. 2, April 1983

USE OF BREMSSTRAHLUNG IN THE MEASUREMENT OF THE EFFICIENCYOF SOLID STATE DETECTORS BELOW 5 keV

Carroll Quarles and Lee EstepDepartment of Physics

Texas Christian University, Fort Worth, Texas

Summary

Atomic-field bremsstrahlung produced by the bom-bardment of atoms by an electron beam of 5-10 keVenergy provides a continuous x-ray source which issuitable for the measurement of the relative effi-ciency of solid state detectors in the energy regionbelow 5 keV. The relative efficiency as a functionof photon energy can be obtained by normalizing theobserved spectrum to the theoretical bremsstrahlungcross section. In this paper we will present an ex-ample of this technique using a thin film target anda gas beam target to illustrate some of the problemsand to demonstrate the potential of this technique.

Introduction

The purpose of this paper is to illustrate howatomic-field bremsstrahlung can be used to determinethe relative efficiency of solid state detectors inthe energy range below 5-10 keV. The techniquedescribed consists of measuring the bremsstrahlungphoton energy spectrum at an angle such as 900produced when an electron beam with 5-10 keV energybombards a thin film target such as carbon or collodionor a gas beam target. The observed bremsstrahlungspectrum is then normalized to the theoretical brem-sstrahlung photon angular distribution d2a/dQdk wherek is the photon energy. The ratio of the experimentaldata to the theory gives the relative efficiency ofthe detector as a function of photon energy. It isthen possible to fit a simple photo-absorption model tothis experimental efficiency. The relative efficiencycan be put on an absolute scale in an independent wayby further normalization to a standard calibratedradioactive source at one photon energy.

Prior work in this area has been done by Palinkasand Schlenk.1 They used 10 keV electrons on a lOpg/cm2carbon target and observed the bremsstrahlung spectrumat 1050. They normalized to the then available photonenergy spectrum,2 which did not take account of the

Fig. 1 Efficiency of a Si(Li)detector versus photonenergy for 5.5 keV elec-trons on a 20pg/cm2 collo-dion target. The curve isthe simple photo-absorptionmodel for the efficiency.The silicon K x-ray peak at1.74 keV is due to a mono-layer of silicon on thetarget. The drop off inthe data at above 3.7 keVis an electron energy losseffect on the bremsstrah-lung spectrum.

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variation of the shape of the photon spectrum with theobserved angle. Using the currently available tabula-tions for the photon angular distribution corrects theirresults by an amount ranging from 0% at 7 keV where theynormalized to 12% at 2 keV.

Theory

The atomic-field bremsstrahlung theory is thecalculation due to Pratt and his co-workers.3 Thetheory is first order in quantum electrodynamics andtreats the bremsstrahlung process as a single electrontransition in a relativistic self-consistent screenedatomic potential. The theory is expected to be validover a wide range of bombarding electron energy, andover the whole range of radiated photon energy and forall atomic numbers. Recently, Kissel, Quarles, andPratt have tabulated the photon angular distribution forelectron energy from 1 to 500 keV, for photon energiesfrom zero to the maximum allowed energy, for selectedatomic numbers from 1 to 92 and for angles from 00 to180° in 50 increments.4 Using this tabulation it ispossible to compute the cross sections needed for thenormalization suggested here.

The theory has been recently tested in the 5 to10 keV range by two experiments using gas beam targetsto eliminate any multiple interaction or energy losseffects.5,6$7 The gases studied include helium, neon,argon, krypton, xenon, mercury and uranium. Except forsome discrepancies for high atomic-number, the theoryis in excellent agreement with the experiments. Thetheory certainly seems adequate for use in the 5-10 keVenergy range from low atomic number targets such ascarbon or collodion (C12H16N4018).

Example of the Technique

To illustrate the technique we will discuss twoexperimental examples. In the first case, 5.5 keVelectrons from a Griffith Model GE50 electron gunbombard a collodion target (20ug/cm2) oriented at

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45 to the beam. The bremsstrahlung spectrum isobserved at 90° to the incident electron beam. Thedetector is a Si(Li) detector with a 30 mm2 area anda 0.3 mil Be window.9 The detector is separated fromthe vacuum by a 2.7 mm air gap and a 0.25 mil mylarwindow. The data for the efficiency are shown inFigure 1. This data was collected in a 2300 s. runat an average electron beam current of 3nA to eliminateany pulse pile-up. The statistical error on thepoints is about 3%. The detector was collimated andplaced 12 inches from the target. The collimationserved to virtually eliminate any background. Thetheoretical cross section for the collodion was com-puted from the tabulation4 by weighting each elementin the molecule by the number of atoms. Thus thebremsstrahlung is computed assuming that each atom inthe molecule contributes incoherently to the totalspectrum. The theoretical shape of the spectrum asa function of photon energy is very insensitive to theelectron bombarding energy in the 5 to 10 keV range,varying by less than 0.01% in the photon energy rangebelow S keV. Furthermore, the shape of the theoreticalspectrum is relatively insensitive to the angularresolution of the detector, varying by less than 0.6%for + 50 around the 90° angle.

The efficiency curve shown in Figure 1 is based ona simple photo-absorption model using the photo-absorp-tion cross sections of Storm and Israel.8 We have fitthe data to determine the photon energy dependence ofthe photo-absorption cross section. The curve isgiven by

E (k)=(1-0.69k-2 76)exp[-3.1jltak-2 79-1.86tBek2 .9

-0.88tmk-3*35-37.96tAuk-2*52]

where ta, tBe, tm and tAu are the air gap, Be, mylarand gold layer thicknesses in-mg/cm2. The factorpreceeding the exponentialcorrects for silicon escape.

The X2 for the fit between the data and thismodel with no free parameters is 44 for 36 degrees offreedom over the photon energy range from 1.2 to 1.5and 1.92 to 3.72 keV (excluding the Si K x-ray peakdescribed below). The nominal thickness of 40pg/cm2was used for the gold layer. A somewhat better fit isobtained by allowing the gold thickness to vary. Thebest fit in this case is for (42.0+0.2)pg/cm2 and theX2 is 42 for 35 degrees of freedom.

Fig. 2 Same as Figure 1 except 5 keVelectrons on a neon gas beamtarget. No electron energyloss effects are observed.The drop off in the dataat about 5 keV is due to theendpoint in the bremsstrah-lung spectrum.

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In Figure 2, results are shown for 5 keV electronson a neon gas beam. Here the statistical error isabout 6% on each point. These data were collected ina 1500 second run with a beam current of 3x10-4A.More channels have been summed to improve the statis-tics in each point. The X2 for the fit to theefficiency model is 37 for 21 degrees of freedom overthe photon energy range from 1.875 to 4.625 keV.

Discussion

Several interesting features can be observedin the data for the collodion film in Figure 1. First,the data deviates from the curve from about 3.7 keV on

up. This is due to energy loss by the electron beam inthe collodion film. Contrast this with the case of theneon target in Figure 2. There the data agrees withthe model up to the endpoint or the maximum possiblephoton energy which equals the incident electronkinetic energy. This sharp drop off is characteristicof the "thin target" bremsstrahlung endpoint.

Second, the peak at 1.74 keV in Figure 1 is asilicon K x-ray peak due to a monolayer of silicon onthe collodion film. This is the result of contamina-tion by pump oil due to inadequate cold trapping. Thesilicon peak can be eliminated by careful attention togood vacuum technique.

Third, we have not made an attempt to fit thegold M-shell edge effect in the efficiency model.This would probably improve the agreement in thecase of the collodion film. Also the correction fromescape loss in silicon is crude and could be improvedin the model.

Conclusions

We have demonstrated the use of a simple techniquewhich can give the relative efficiency of a solid statedetector as a function of photon energy. We believethis technique to be as precise as the conventionaltechnique using calibrated sources. It requires onlysimple apparatus to use and permits the entire effi-ciency curve to be measured in one run with goodstatistics and in a set up which can simulate if notduplicate the actual experimental environment inwhich the detector will operate. With some care, thebackground can be essentially negligible. Thinfilms are probably more useful than gas beams. Carbon

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is to be preferred, but a collodion film can bequickly and inexpensively made in any lab.

Further work is planned to determine the preci-sion achievable with this technique. Also, we plan tocontinue measurement of the bremsstrahlung spectrumfor a wide variety of parameters to further test thetheory.

References

1. J. Palinkas and B. Schlenk, Nucl. Instrum. Meth.169, 493 (1980).

2. R. H. Pratt et al., At. Data Nucl. Data Tables 20,175 (1977).

3. For a review and earlier references see: R. H.Pratt, Electron Bremsstrahlung X80: Theory andRecent Developments, Inner-Shell and X-Ray Physics

of Atoms and Solids. Eds. D. J. Fabian, H. Klein-poppen and L. M. Watson, (Plenum Publ. Co., 1981).

4. Lynn Kissel, C. A. Quarles and R. R. Pratt, At.Data Nucl. Data Tables 28, (to be published).

5. R. Hippler, K. Saeed, I. McGregor, and H. Klein-poppen, Phys. Rev. Letters 46, 1622 (1981).

6. Mars Semaan and C. A. Quarles, Phys. Rev.,A 24,2280 (1981).

7. Mars Semaan and C. A. Quarles, Phys. Rev. A (to bepublished).

8. E. Storm and H. Israel, Nucl. Data Tables A 7, 565(1970).

9. We want to express appreciation to Dr. Bill Tittlefor the loan of the Si(Li) detector.