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1176 IEEE Transactions on Nuclear Science, Vol. 36, No. 1, February 1989

MONTE CARLO SIMULATION OF GAMMA RAYSPECTRA FROM SEMICONDUCTOR DETECTORSF.Olschner, J.C. Lund, and I . SternRadiation Monitoring Devices, Inc.44 Hunt St., Watertown, M A 02172

INTRODUCTIONAlthough the physical effects occurring withinsemiconductor gamma ray detectors are separately wellunderstood, it is not always clear exactly how the effectscombine to create the sometimes complicated gamma ray pulseheight spectra measured in the laboratory. A useful tool to

study this is a computerized simulation of the gamma raydetector. In such simulations various physical effects can be"turned on" or "off', allowing the effects to be studiedseparately. Reliable simulation algorithms can be used tooptimize a detector geometry or configuration, significantlyreducing the experimental effort usually associated withdetector development.Pulse height spectrum simulations can also be useful inthe creation of detector response matrices. These matrices are

necessary to reconstruct actual energy spectra from themeasured energy spectra.A lthough other methods have been used [11we chose touse a Morite Cw-lo type algorithm to simulate detectorperformance. M onte Carlo is well suited to simulate thenatural stochastic processes in gamma ray interactions [2].SIMUL ATED EFFECTS

The simulations in this study were conducted assuming"bulk type" radiation detectors. Bulk detectors consist ofparallel contacts on opposite sides of i i uniform high resistivitysemiconducting crystal. An applied potential yields a uniformelectric field within the detector. In this study the detectorswere assumed to be of rectangular geometry, but the algorithmcould easily be adapted for detectors of other shapes.The M onte Carlo simulation program described herewas written in Pascal [3] and run on an IBM PC compatiblemicrocomputer with numeric coprocessor. Over 15events persecond could be simulated. The various physical eventsoccurring within a semiconductor gamma ray detector aresimulated in a naturally sequential manner. Specifically, thealgorithm simulates such effects as exponentially absorbedradiation, the possibilities of multiple Compton scatteringwithin the detector, charge carrier trapping, and electronicnoise (Gaussian). A point source of gamma radiation in therange of a few keV to a few M eV is assumed, as is the absenceof any material other than the detector. The algorithm could beadapted, however, to simulate extended sources and scatteringfrom nearby materials.

S IMULAT ION MECHANICSSubroutines within the simulation program fall into twocategories. In the first are subroutines which compute theenergy deposition within the detector due to the incidentgamma rays. These take into account Compton andphotoelectric interactions and use methods described below.

Subroutines in the second category compute the amplitudes ofthe charge pulses due to the previously calculated energydeposition. These subroutines are based on a model ofsemiconductor detector performance that considers thetrapping of electrons and holes in the semiconductor detector.As is diagrammed in figure 1, incoming monoenergeticgamma rays interact within the detector at random positionshaving interaction probabilities consistent with exponentiallyabsorbed radiation. T he type of interaction (photoelectric orCompton) is randomly determined, consistent with theirrelative probabilities at the specified energy.

IDetermlne where th ei ncomngga mma r ayl a StoppedCalcul ate the Determine

ga mma rayharqe using interactshe Hecht eqn.

De\erminethedi~ection

chergeu5mg the1

total coll ected charge 1

Figure 1.simulation utilized in this study.Flow chart illustrating the processes of gamma ray spectrum

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T he charge collection effi ciency within the detector is afunction of the position within the detector and isgiven by

Lvhere U/Q0 s the charge collection efficiency, x is the distancefrom the negative contact, d is the detector thickness, V is thebias voltage, and ( p ~ ) ~nd ( p ~ ) ~re the mobility-trapping timeproducts for electrons and holes respectively [4>5,6.7]. V aluestor ( p ~ ) ~nd ( p ~ ) ~ay be measured beforehand or they mayhe determined by fitting simulated spectra to measured spectra.

I f it is determined that ii Compton interaction occurs,the direction of the scattered gamma ray is randomlydetermined, consistent with the probabilities predicted byK lein-Nishina [SI. T he ener g from Compton electrons isassumed to be quickly absorbed by the semiconductor, withtheir enerLy going directly i nto the production of f ree chargecarriers (electron-hole pairs) within the detector. This is alsoassumed to he true of the photoelectrons. Using the position ofeach of these interactions within the detector. the chargecollection efficiency is calculated from ecpicrfion1. The "chargecollected" for this interaction is calculated by multiplying thecharge collection efficiency by the energy of the scatteredelectron.lJ sing the scattered gamma ray's chosen direction, i tsnext interaction point is randomly chosen in ii mannerconsistent with the fact that such radiation is also exponentiallyiibsorbed. I f this interaction point lies outside the detectorhoundaries, the scattered gamma ray is considered to haveescaped. If not. the type of interaction must then be chosen(photoelectric or Conipton), etc.. This process continues untilthe gainma rays are photoelectrically absorbed OJ they escape.The total "charge collected" is then calculated, adding up thisquantity from each of the interactions. Finally this quantity isstored (or "binned") in a histogram which serves a s the finalpul!,e height spectrum af ter many events are simulated.

OTHER S IMULAT ION P ROG RAMSThere exist a few very large M onte Carlo photon andparticle transport simulation computer programs [9.10,11,12].These programs are very detail ed and simulate many physicaleffects. They accurately accomplish the task of computing thepxitions within the detector of particle or gamma interactionsand the resulting enerby deposited to the detector at thesepoints. Swierkowski [I31has used SANDYL [Y ] to simulate thepulse height spectra of high-Z detectors irradiated by '37Cs(662 keV gamma rays) having different geometries with someThese programs have a few drawbacks. however. They

are quite large (usually tens of thousands of lines ofFORTRA N code) and require fast computers with largcmemories. These programs usually run fairly slowly, althoughthe run time is dependent upon the degree of complexity of theproblem being simulated.

success.

These large programs are also quite comprehensive, inthat different types of radiation are simulated over large energyranges. T he simulations performed iiz this slicdy are ratherspecialized in that only gamma rays froin a few keV toapproximately 1 M eV are accurately simulated. In this enerkyrange photoelectric and Compton interactions predominate.For this reason our simulations. which were performed underthese circumstances. agree well with measured semiconductorganimi ray detector pulse height spectra.

COMPARISON OF THE S IMUL ATION WITHLABORATORY RESULTST he simulations in this study were made usingparameters identical to detectors availabk in the laboratory sothat comparisons could be made between the simulations andactual semiconductor gamnia ray pulse height spectra.Cncimium telluri de (C dT e) semiconductor detectors were used

for the comparison. F&ire -3 shows ii 137Cs 662 keV gammaray) pulse height spectrum overlapping ; M onte Carlosimulation. F@re 3 is a 57c01'2 and 136 kev garnnia rays)pulse height spectrum and simulation. The results of theCO inp Ute r si nU at o i agree we \vith expe ri ni e n ta spectra.however some anomalies were ohserved.

0a- 4 -t!? 3 --E 2 -30 1 -

0 10 200 400 600collected energy (keV)2.0 I

o -measu red-s imulated

-1.0 -a+07 0.5 -I?3U

n n l . ?LU.U -50 400 450 500 550 600 650collected energy (keV)Fiprc 2. 14ca\urcd '"Cs (602 kcV pininia ray) pul w height spectrumovcr1,ipping ;I \ in iula~ion. .A CdTe detector \w\ used to nieiihiirc the\p i ' itt i in i. the dimcngiona 01 \\hieh \\ere 1 nini thick s10mmwidth x 10 ninldepth. Bia\ vollagc = 3 H I \'. (, UT), =?slO-' cni2V ~' . 1 1 ~ ) ~ ~7u10 ' ni' V".Elcitronic n o i w i n thc CdTc dclcclor \\'I\ mca\ured to he 6 Lev (FWHM),ho\\cicr the aimulation hc\t fi t the d ~ t a hen 3 kcV (FLVHM) of Gaussianhroiidcning \%a$used. Figure 3 ho\vs a detail of ligurc 21,lluhli-ating thc\ c r y ~ o o dgrccment hct\\c.cn the hpcctra ohwmcd at highcr energies.

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As can be seen in the pulse height spectra in figures 2arid 3, the fit between simulated and measured pulse heightspectra is not as good at lower energies. There are twoprobable reasons for this discrepancy. T he first, and probablymost significant, is our omission of charge carrier detrappingeffects from the simulation. T he "bump" in the measured 57C0spectrum in figure 3 is almost certainly due to charge carrierdetrappi ng because it's position was observed to change withthe li near amplifier's time constants. A lthough charge carrierdetrapping effects are difficult to predict [14], we feel thatcomputerized simulations may afford numerical methodseffective in determining a solution and efforts are currentlyunderway to include detrapping in our simulations.

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0.0I20 40 60 80 100 120 140collected energy (keV)Figure 3. M easured 57Co (122 and 136 keV gamma rays) pulse heightspectrum ovcrlapping a simulation. A CdT e detector was used to measurethe spectrum, the dimensions of which were 2 mm thick x10 mmwidth x 10mmdepth. Bias voltage =250V. @T ) ~=2x10-' cm2V I , @),, =7~10-~m2V-'. Electronic noise in the CdTe detector was measured to be 6 keV(FWHM), which is equal to the amount of Gaussian broadcning simulated.Compton evcnts arenot prominent in thi s spcctrum, as the Compton shoulderencrgy is approximately40keV.A nother possible cause for the discrepancy betweensimulated and measured spectra are scattered gamma rays fromnearby objects (backscatter) which are measured but notsimulated. These photons would enhance the low energy

region of the pulse height spectrum. Fluorescence X -rayescape may also account for some of the discrepancy at lowenergy.Noise in the detection electronics is certainly a source ofGaussian broadening in the measured pulse height spectra,however other more subtle sources may also exist.Inhomogeneities in p7, for example, will result in broadenedpulse height spectra. In the simulations, the broadeningparameter is not determinable a priori, but is fit to themeasured data. In fact,measurement of a detector's pulse height spectra has proven tobe an simple method of determining p7 in a semiconductordetector material.

T he same is true for (p7), and ( p ~ ) ~

CONCLUSIONSComputer simulations of semiconductor gamma raydetector pulse height spectra are useful for a number ofreasons. Some of these are:

1.) T he response matrix [15] of a detector can becalculated by simulating monoenergetic gamma rayspectra at various energies.

2.) M easurement of certain detector properties can bedetermined by fi tting simulations to measured pulseheight spectra.Optimal detector geometries can be determinedquickly by simulation.Diffi cult or impractical to buil d detectors can bestudied without actual construction.

3.)

4.)In this study, M onte Carlo techniques were used tosimulate gamma ray pulse height spectra from rectangularly

shaped CdT e detectors in the energy range of a few keV toapproximately 1M eV. T he simulation results were found toagree well with measured C dT e gamma ray pulse heightspectra.Deviations of the simulations from the measured spectramay be due to physical effects which are not simulated. Theseinclude:1.)2.)3.) X-ray f luorescence4.) A uger electron production5.)6.) Coherent scattering

Scattering f rom nearby objects in the laboratoryCharge detrapping effects within the detector

Pair production (if Egamma>MeV)

A dvantages of this simulation method are thecompactness of the code (allowing the use of microcomputers)and the speed of operation (approximately 15 events persecond).We would l ike to acknowl edge helpful discussions withFrank Sinclair and M ike Squil lante, and to thank J im K ozlotskyfor his help in preparing this manuscript.

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REFERENC ESR. Bell, Nucl. Inst. and M eth., 93,p.A-2, (1971).M . K alos and P. Whitlock, M onte Carlo M ethods, p.3, Wiley, (1986).Borland International Inc., Turbo Pascal 3.0, (ScottsValley, CA , 1983).K. Hecht, 2. hysik, 77,235, (1932).R. H ofstadter, Nucleonics, 9, (1949).W. A kutagawa and K. Zanio, J . A ppl. Phys., 40, p.3838, (1969).R.C . Whited, M .M . Schieber, Nucl. I nst. and Meth.162. p 133, (1979).L.L. Carter and E.D. Cashwell, Particle-Trans"Simulation with the M onte Carlo M ethod, ERDA ,Oak Ridge, TN, (1975).H.M . Colbert, SA ND Y L : A Computer Program forCalculatinP Combined Photon-Electron Transportin Complex Systems, Sandia R eport SL L -74-0012,(1974).J.F. Briesmeister, ed. M CN P- A General M onteCarlo for Neutron and Photon Transport, LosA lanios National Laboratory Report L A-7396-M(Rev. 2) (1986).W.R. Nelson, H. Hirayama, and D.W.O. Rogers,The EGS4 C ode System, SLA C Report SLA C-265(1985).J .A . Halbleib, T .A. Mehlhorn, ITS: T he IntegratedTI GE R Series of Coupled E lectronPhoton M onteCarlo Transport Codes, Sandia Report SANDS%0573, (1984).S.P Swierkowski, I EE E T rans. Nuc. Sci., NS-23 p.131. (1976).K . Zanio, "Cadmium Telluride", in Semiconductorsand Semimetals. V ol. 13,ed. by R.K . Willardson andA.C. Beer, p. 178. Academic Press, (1978).G.F. Knoll, Radiation Detection and M easurement,p. 733, Wiley, (1979).