Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–22

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Nuclear Instruments and Methods inPhysics Research A

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journal homepage: www.elsevier.com/locate/nima

Performance of Geant4 in simulating semiconductor particle detectorresponse in the energy range below 1 MeV

G. Soti a,n, F. Wauters a,1, M. Breitenfeldt a, P. Finlay a, I.S. Kraev a, A. Knecht a,b,T. Porobić a, D. Zákoucký c, N. Severijns a

a Instituut voor Kern-en Stralingsfysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgiumb PH Department, CERN, CH-1211 Geneva 23, Switzerlandc Nuclear Physics Institute, ASCR, 250 68 Rež, Czech Republic

a r t i c l e i n f o

Article history:Received 12 April 2013Received in revised form28 May 2013Accepted 13 June 2013Available online 24 June 2013

Keywords:Geant4PIPS detectorsHPGe particle detectorsElectron backscattering

02/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.nima.2013.06.047

esponding author.ail addresses: gergelj.soti@fys.kuleuven.be, sotrrent address: Center for Experimental Nucleity of Washington, Seattle, Washington 98195

a b s t r a c t

Geant4 simulations play a crucial role in the analysis and interpretation of experiments providing low energyprecision tests of the Standard Model. This paper focuses on the accuracy of the description of the electronprocesses in the energy range between 100 and 1000 keV. The effect of the different simulation parametersand multiple scattering models on the backscattering coefficients is investigated. Simulations of the responseof HPGe and passivated implanted planar Si detectors to β particles are compared to experimental results. Anoverall good agreement is found between Geant4 simulations and experimental data.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The search for physics beyond the Standard Model takes manyforms. At the high energy frontier accelerators such as the LHC areable to produce new particles which could point toward newphysics. The other, precision frontier relies on measurements ofdifferent observables, as e.g. in neutron and nuclear β decay, wherea deviation from the Standard Model value is an unambiguous andmodel independent sign of new physics [1–6]. In order to furtherincrease the precision of such measurements all possible systema-tic effects need to be evaluated, which often include Monte Carlosimulations such as the Geant4 simulation toolkit [7]. Amongothers it is widely used in neutron and nuclear correlationmeasurements [8–11] and in searches for neutrinoless double-βdecay [12,13].

The majority of these experiments are focusing on tracking anddetection of electrons with typical β decay energies (100 keV–1 MeV) where one of the dominant systematic effects is theelectron scattering from energy sensitive detectors. With therelative precision of the Standard Model tests in neutron andnuclear β decay reaching the sub-percent level the accuracy of the

ll rights reserved.

i.gergely@gmail.com (G. Soti).ar Physics and Astrophysics,, USA.

Geant4 models needs to be re-evaluated and compared to new,high precision and high quality experimental data.

This work focuses on the influence of the various Geant4models and their parameters on the simulated values of thebackscattering coefficients. It also investigates the quality withwhich experimental spectra of different β decaying isotopes arereproduced. The results can be used to assign systematic errors tothe simulations and also to estimate the systematic differencebetween simulated and experimental spectra.

2. Relevant Geant4 processes

Geant4 [7] is a toolkit for simulating the passage of particlesthrough matter. It was developed with the experiments at the LHCaccelerator in mind and is therefore tuned to simulate high energyphysics experiments. However, low-energy weak interaction experi-ments in neutron and nuclear β decay that are dealing with βparticles of around 1 MeV kinetic energy typically, can also benefitfrom information provided by Geant4. At these low energies thephysical processes involved are greatly reduced in number: practi-cally only the electromagnetic interaction remains active. In thispaper we will therefore focus on the electromagnetic processes ofGeant4 [14,15]. Furthermore, we will focus on processes related toelectrons. The relevant processes for this energy range used inGeant4 are the photoelectric effect, Compton-scattering and paircreation for γ rays, while for electrons ionization, bremsstrahlung and

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–2212

scattering processes are included. Naturally all these processes aredescribed by models, based on our current understanding of nature,but for practical purposes there will always be a compromisebetween realistic calculation time and the desired accuracy. A setof these models is called a physics list, and since version 9.3 of theGeant4 code these come in three flavors:

1.

Standard—used for high energy physics experiments [16,17],but applicable to energies from 1 keV to 10 TeV [14].

2.

Livermore—Extends the validity of the electromagnetic pro-cesses down to 250 eV, with more accurate descriptions ofatomic effects and direct use of cross-section data (the Stan-dard physics list uses a parameterisation of these). This packageused to be called the Low Energy physics list in version 9.0 andearlier [18].

3.

Penelope—Being developed based on the Penelope simulationpackage [19], applicable to energies down to a few hundred eV[20]. Note that this package does not include the Penelope-specific electron multiple scattering algorithm.

It is to be noted that both Livermore and Penelope physics listsprovide their own versions of several processes, such as ionizationor bremsstrahlung [20,21]. However, the multiple scattering pro-cesses are shared with the Standard physics list.

The multiple Rutherford scattering of electrons in matter isdescribed by multiple scattering theories developed by Goudsmitand Saunderson [22] and later Lewis [23]. Both of these theoriesdescribe the individual scattering events by using Legendre poly-nomials, with their additive properties leading to an analyticalsolution of the final deflection angle after several scatteringevents. The Lewis theory provides the moments of the spatialdisplacement distribution as well.

Simulation of the individual Rutherford scattering events inGeant4 is possible by registering the Single Scattering [24,25]process to electrons and positrons. However, this is only practicalfor situations where the number of electron–electron collisions islow, e.g. for thin foils or low energy electrons. Since theseconditions are in general not fulfilled, the multiple scattering(MSC) models were also implemented [26,20]. These modelsaverage out the individual scattering events thus allowing thesteps to be longer and the simulation to run faster. The MSCmodels should therefore provide information about the angulardeflection, true path length correction and spatial displacement ofthe electron. These models are not exact and are responsible formost of the electron transport uncertainties [20], affecting quan-tities such as the backscattering coefficient.

The recent MSC models implemented in Geant4 are specific to aparticle type, i.e. electrons, hadrons and muons. In this paper we willfocus on the electron MSC models available in Geant4 version 9.5:

�

Single Scattering—Simulates individual Rutherford scatteringevents, based on screened nuclear potentials, according to thePenelope code [27].

�

Urban MSC model—The default model within Geant4 is basedon the Lewis MSC theory [23], and is applicable to all particles.It uses model functions chosen such that they yield the sameangular and spatial distributions as the Lewis theory. Further-more, it uses different parameterisations of the central and tailpart of the scattering angle distribution [25]. Its performancehas been validated against data obtained in thin foil transmis-sion experiments [28]. However, the majority of these experi-ments were carried out using primary beams of energies above1 MeV.

�

Goudsmit–Saunderson MSC model—Based on the theorydeveloped by Goudsmit and Saunderson [22] and is applicableonly to electrons and positrons. It uses a database of cross-

sections generated by the ELSEPA code [29] and a samplingalgorithm similar to the one presented in Ref. [30].

It is to be noted that the choice of the MSC model is independentof the physics list.

When simulating low energy experiments as e.g. β decay, onefirst has to verify that the values of the various simulationparameters are suited for this energy range. The relevant para-meters are [31,32,25]:

�

Cut for Secondaries (CFS)—Controls the way secondary parti-cles are created, i.e. if a secondary particle would traverse in agiven material a distance less than the CFS, it is not created butits energy is deposited locally. Therefore the value of thisparameter should be smaller than the linear dimensions ofthe smallest “sensitive” geometrical volume. Its default value is1 mm, however, with typical detector thicknesses of about1 mm as used in low energy experiments this value is obviouslytoo large and a CFS value of e.g. 1 μm is more suited, as wasobserved before [33];

�

FR—Limits the length of steps to a fraction of the electron meanfree path. The default value is 0.04;

�

FG—Determines the minimum number of steps in a givenvolume. The default value is 2.5;

�

Skin—Dimensionless factor which defines a region nearvolume boundaries where single Coulomb scattering is applied.The thickness of this region is given by λ � Skin, where λ is theelectron mean free path. The default value of this parameteris 3.

First, the performance of Geant4 with respect to the electronbackscattering will be investigated, considering the differentphysics lists, multiple scattering models and simulation para-meters. Next, simulated spectra for different isotopes will becompared to experimental data obtained with both planar highpurity germanium (HPGe) detectors and passivated implantedplanar silicon (PIPS) detectors.

3. Backscatter comparisons

3.1. Introduction and literature review

In order to validate the Geant4 electron processes one needssimple experiments (both in terms of geometry and of the physicsinvolved) and high-quality data. A rather simple experimentalobservable related to electron processes is the backscatteringcoefficient. When an electron backscatters from the detector itdeposits only part of its energy and then escapes from thedetector, thereby distorting the shape of the measured electronspectrum. By simulating such a rather straightforward experimentthe obtained backscattering coefficients can be directly comparedto values cited in the literature.

Tabata et al. [34] gave an empirical formula based on availableexperimental data (see Ref. [34] and the references therein). Theresulting backscattering coefficients for Si are shown as the shadedband in Fig. 1. Note that the uncertainties of the fitted parameterslisted in Ref. [34] induce relative uncertainties on the backscatter-ing coefficients of about 10% (width of the shaded band). Seltzeret al. [36] presented backscattering and transmission results forfoils of various materials. The Geant4 MSC models were validatedagainst these data. However, no data for Si or Ge were included inRef. [36]. The most recent papers about backscattering of lowenergy electrons are by Martin et al. [35,37]. These authorsmeasured the electron backscattering coefficients for silicon,beryllium and organic scintillators in the energy range from

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Fig. 2. Backscattering coefficient in function of the incoming electron energy. Dataare shown for the Standard, Livermore and Penelope physics lists, using the defaultMSC model.

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Fig. 3. Backscattering coefficient as a function of the incoming electron energy,calculated with the Urban, Goudsmit–Saunderson and Single Scattering modelswithin the Standard physics list.

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Fig. 1. Backscattering coefficients for normal incidence electrons on Si. The shadedregion marked Tabata is the 1s interval of the backscattering coefficient calculatedusing the formulas given by Tabata [34]. The data points are experimental resultsfrom Martin et al. [35], where the “current integration” and “Si detector” refer to themethods used to arrive to the results.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–22 13

40 keV to 130 keV, and their results for Si are also shown in Fig. 1.It should be noted that no high-precision backscattering ortransmission data for Si and Ge in the energy range between150 keV and 1000 keV are currently available. However, the resultsfrom Martin et al. [35,37] as well as our own previous work[8,33,38,39] give good confidence in Geant4's ability to reproduceexperimental data with an absolute precision that is typically ofthe order of 1%.

3.2. Simulations

As a first step in investigating the performance of Geant4 withrespect to the electron backscattering we simulated a monoener-getic electron beam hitting a 1 mm thick slab of pure Si. Simula-tions were performed using Geant4 version 9.5 for all MSC modelsand the influence of the different simulation parameters listed inSection 2 were investigated as well.

3.2.1. Physics listsThe backscattering coefficient as a function of energy obtained

for the different physics lists is shown in Fig. 2. The differences arevery small, with the Livermore and Standard physics lists provid-ing almost identical results, demonstrating that for these simula-tions the usage of the low-energy packages (Livermore andPenelope) is not absolutely required. A notable feature of all threecurves is the decrease of the backscattering coefficient below200 keV, which is unrealistic. This is an artifact of the UrbanMSC model, as will be demonstrated further on.

3.2.2. Multiple scattering modelsAs the backscattering results do not significantly depend on the

physics list used, we will further use the Standard physics list tostudy the MSC models. As the backscattering coefficient dependson the accurate sampling of large scattering angles, we can expectlarger differences between the condensed MSC models (Urban andGoudsmit–Saunderson) and the Single Scattering process. Theresults for all three models are shown in Fig. 3. For the Urbanmodel a decrease in the backscattering coefficient is observedbelow 200 keV. This, in combination with other possibly uniden-tified effects, contributes to the fact that the difference betweensimulated and experimental spectra rises up to 50% in the energy

region below 100 keV (see Sections 5 and 6). Further, a constantoffset is visible compared to the other models as well as to theempirical relation; the reason for this is unclear. The SingleScattering model shows more stable behavior and also yieldsvalues closer to the central values obtained from the empiricalrelation of Tabata et al. [34], although the 10% uncertainty on thevalues calculated with this relation does not exclude the two othermodels. The Goudsmit–Saunderson model is found to exhibit aclear “staggering” effect which is not expected from physicsgrounds, rendering this model less interesting for applicationsthat require high precision.

3.2.3. Simulation parametersTo investigate the effect of the different simulation parameters

on the backscattering coefficient the Urban MSC model was usedas it is the default model and also requires the smallest calculationtime. The dependence of the backscattering coefficients on the CFSvalue is shown in Fig. 4. The fact that the backscattering coefficientincreases with decreasing CFS value is expected (the smaller theCFS the more low energy secondaries are created). However, for avalue of 1 μm it reaches the edge of the 1s band of Tabata. Tofurther investigate this difference, spectra of deposited energies

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Fig. 5. Spectrum of deposited energies for 500 keV incoming electrons. The defaultvalue for CFS of 1 mm is compared to our recommended value of 1 μm.

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Fig. 6. Backscattering coefficient as a function of the incoming electron energy fordifferent values of the FR parameter. Simulations were performed using theStandard physics list with the Urban MSC model.

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Fig. 7. Spectrum of deposited energies for pure backscatter events for 500 keVnormal incident electrons. The default value for FR of 0.04 is compared to the valueof 0.002.

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Fig. 4. Backscattering coefficient as a function of the incoming electron energy fordifferent values of the CFS parameter. Simulations were performed using theStandard physics list with the Urban MSC model.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–2214

for the backscattered events are shown in Fig. 5 for the extremecases CFS¼ 1 μm and CFS¼1 mm. The effect of the different valuesof the CFS parameter is as expected, i.e. for smaller CFS values theprobability for the electron to deposit a higher fraction of its initialenergy increases (feature “A” in Fig. 5). Despite the slightly worseagreement between the Tabata values [34] and the simulated datafor CFS¼ 1 μm, we will continue to use the value of 1 μm for thisparameter as it is considered to be more realistic for our purposes(e.g. the detector dead layer thicknesses are typically of the orderof several 100 nm).

Simulation results for different values of the FR parameter areshown in Fig. 6. The backscattering coefficient is found to saturatewhen the FR parameter drops below 0.002 (see Fig. 6). Thecorresponding spectrum of deposited energies for the backscat-tered electrons (Fig. 7) shows less events for incident electronsdepositing only a small fraction of their initial energy (feature “A”in Fig. 7) in the detector before being backscattered. Further, forFR¼0.04 a sharp drop is observed below about 30 keV, which isnot physical. Therefore, an FR value between 0.01 and 0.002 seemsrealistic. A dedicated experiment focusing on these effects, so as todetermine the best value, would be welcome.

Simulations performed for different values of the FG and Skinparameters did not result in significant changes of the back-scattering coefficient. Therefore, in subsequent simulations theirdefault values (see Section 2) were used.

3.3. Conclusions on the backscattering coefficients

The different MSC models and simulation parameters influencethe backscattering coefficient at the 10% level, which is approxi-mately equal to the uncertainty of the empirical relation of Tabataet al. [34]. The default value of the CFS parameter of 1 mm is toolarge if one uses typical particle detectors with thicknesses up toseveral mm. Furthermore, the typical dead layer thicknesses aremuch smaller, such that a more realistic value is around 1 μm.Simulations using this value for the CFS parameter produce back-scattering coefficients in agreement with the results from theempirical relation. Based solely on the backscattering coefficientsthe best value for FR cannot be determined unambiguously. Wetherefore fix it for the time being at the default value of 0.04. TheSingle Scattering model agrees the best with the empiricalequation of Tabata, but unfortunately it requires approximately10 times more computer time than the Urban or the Goudsmit–Saunderson models.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–22 15

Since the MSC models need to provide the angular deflection(scattering angle) after each step, a suitable benchmark would behigh precision data on the angular distribution of electrons aftertransmission through thin foils of various thicknesses [40]. We arein the process of preparing such an experiment.

Fig. 8. Dimensions of the 15/4 HPGe particle detector. All numbers are inunits of mm.

4. Simulation of detector response

A Geant4 simulation records the energy deposited in a speci-fied geometrical volume. Such a simulated spectrum, however,cannot be directly compared to the measured spectrum sinceseveral instrumental effects as well as the decay scheme of theisotope considered still have to be taken into account.

4.1. Energy resolution

Geant4 does not take into account effects such as chargetrapping in the detector or noise originating in the preamplifierand in the amplifier, all of which determine the energy resolutionobserved. Although Geant4 provides built-in classes to addressthese issues, we prefer another approach. The net effect of theserandom changes to the signal is best described by a Gaussianspread of the final simulated spectrum from Geant4. For the widthof the Gaussian used to convolute that spectrum we use a valuedetermined by a χ2 fit to the conversion electron peaks from thedecay of 207Bi at 482 and 976 keV.

4.2. Pile-up

As will be seen in the following sections, even for a pure βspectrum, i.e. with no γ�rays being present in the decay scheme,often events above the endpoint energy are observed (see e.g.Fig. 11). This is due to detector event pile-up, an artifact of signalprocessing. This effect can be accounted for in several ways. Weprefer to deal with this in post-processing, since it is then easy tochange the pile-up probability thus accounting for changes in thesource activity as, e.g., occurs in on-line experiments. One thenintroduces a probability that two random events from the spec-trum are summed together. The magnitude of this probability isdetermined by the best fit to the region of the experimentalspectrum above the β endpoint energy, or if a pulser peak ispresent, by the pulser peak-to-tail ratio.

4.3. Geant4 radioactive decay

Geant4 handles nuclear decays via the G4RadioactiveDecayprocess. This includes the different decay modes with theirbranching ratios and automatically generates decay products, suchas α or β particles. Considering β�decay, besides the phase spacefactors only the Fermi function is implemented however. There-fore, in the studies concerning β decaying isotopes a custom madecode was used [33] with the Fermi function and all higherorder corrections implemented according to the prescriptions ofWilkinson [41–44].

5. Geant4 performance for planar HPGe detectors

Custom made planar HPGe detectors were developed [45,46]for low temperature nuclear orientation β�asymmetry measure-ments. They were used in an experiment with 114In [38] and in the67/68Cu experiment at ISOLDE, CERN [47]. All of them wereextensively tested [48], and in this paper we will focus on the15/4 detector. Fig. 8 shows a sketch of the detector with all itsdimensions noted. The detector has its front electrode made with

boron implantation and the thickness of this dead layer isestimated to be ∼100 nm. The thickness of the Li diffused deadlayer at the rear electrode side of the detector was measured to bein the range of 0.7–0.9 mm. Simulations showed that a variation of0.1 mm in this thickness does not change the response of thedetector significantly. The sensitive area of the detector wasmodeled according to the results of a series of measurementswith collimators of different size, further supported by COMSOL-Multiphysics [49] simulations.

The detector was positioned inside a vacuum chamber and a1 mm thick Cu collimator with a 12 mm diameter circular hole wasmounted in front of it. The role of this collimator is to stop theelectrons arriving at the edge of the detector where the electricfield might not be uniform and thus not all the charge createdwould be collected. The response of the detector was extensivelytested at a temperature of 77 K with four different radioactivesources, i.e. 60Co, 85Kr, 90Y and 207Bi. The 207Bi source wassandwiched between two 5:325 μm thick Ti foils in which theconversion electrons loose only about 2 keV energy. The 60Cosource was sandwiched between two, 10 μm thick mylar foils,leading to an energy loss for electrons of about 3–4 keV. The 85Krsource was a 0.05 mm thick iron foil in which the radioactivenuclei were implanted up to a depth of around 15 nm. The 90Ysource was prepared in-house by drying a small drop of liquidsolution containing 90Sr (which decays to 90Y) inside a hole in apiece of aluminum of 25�10�1 mm3. Thereafter the activity wascovered with a 0.1 mm thin layer of epoxy.

5.1. Comparisons with Geant4

The detailed geometry of the entire setup (vacuum chamber,support structures, sources and detectors, see Fig. 9) used tomeasure electron spectra with the different sources was imple-mented in Geant4. Simulations were then performed for eachdetector–source combination and the resulting histograms werenormalized to the number of counts in an energy range dependingon the isotope. For comparing the experiment to the simulatedspectra we used the reduced χ2 defined as

χ2red ¼1ν∑i

ðyexpi −ysimi Þ2s2i;exp þ s2i;sim

ð1Þ

with ν the number of degrees of freedom, yexpi and ysimi the contentof the ith bin in the experimental and simulated spectrum,respectively, and s the associated uncertainty. In the ideal caseχ2red should be equal to unity. However, the measurements

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Fig. 10. Comparison between experimental and simulated spectra of 207Bi, for the15/4 detector. The two main γ lines (at 569.7 keV and 1063 keV) are visible (highestenergetic peak of the groups around 500 keV and 1000 keV), together with their K,L (and M) conversion electrons. Both γ rays generate Compton edges which arelocated at 394 and 857 keV, respectively. The K α and K β X-ray lines are at 74 keVand at 85 keV. The spectra were normalized in the energy region from 50 to1200 keV.

Fig. 9. Sketch of the experimental setup used to measure electron spectra ofdifferent isotopes with HPGe detectors. The bottom plate of the vacuum chamber isconnected to a liquid nitrogen bath allowing the detectors to be cooled to 77 K. Theradioactive source is mounted on a rotating plate so it can be positioned above anyof the detectors without the need for opening the system.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–2216

presented in this paper were performed to investigate the impactof the different Geant4 parameters, so that differences betweenexperimental data and simulations larger than the statisticaluncertainties can be expected. Although the χ2red value can thusnot be expected to be around unity, it can, however, still beconsidered as a relative figure of merit between simulations fordifferent parameters or models being used.

5.1.1. 207BiReproducing the experimental spectrum obtained for this

isotope is the most demanding job for Geant4 as the decay of207Bi produces X-rays, conversion electrons and γ rays over a wideenergy range. Spectra obtained with these thin detectors aredominated by the conversion electrons, while the γ rays contributemainly via the Compton effect. As this isotope decays via electroncapture and because of its relatively complex decay scheme thestandard radioactive decay module of Geant4 was used in thesimulations. In Fig. 10 the experimental and simulated spectra forthe 15/4 detector are compared. Although the overall features arewell reproduced for energies above 150 keV, clear differencesbetween simulation and experiment are observed in some parts,especially near the Compton edges which are overestimated by thesimulation.

The distinct difference between simulation and experiment inthe spectrum of 207Bi near the Compton edge of the two γ raysmight be in part due to the inaccuracy of the Compton scatteringcross-sections, which is further emphasized by the relatively highZ value of Ge. As the γ processes within Geant4 have beenvalidated at the level of several percent [50] the reason for theobserved difference is most probably an interplay between severaleffects, such as the e.g. fine details of the Compton scatteringprocess and the detection of the resulting electron. Note that noclear dependence of the Compton-edge intensity on the detectorthickness was observed. It is to be noted that this effect was alsoobserved when comparing spectra measured with PIPS detectors(see Section 6 and Fig. 19), although less pronounced.

It was found that simulations performed with the Penelope orLivermore physics lists produced a smoother Compton edge,similar to Fig. 19. However, the differences between the Standardand Penelope (or Livermore) physics lists is significantly smallerthan the difference between simulation and experiment.

5.1.2. 85KrThis isotope is suitable to check detector response to relatively

low energy β particles (the endpoint energy of the 85Kr decay isE0 ¼ 687 keV), without any disturbance from γ rays. However, theradioactive decay module of Geant4 does not generate the correctspectrum shape for this isotope as it does not decay via an allowedβ transition but via a so-called first forbidden unique β transition,the spectrum shape of which is not included in Geant4. For thistype of transitions the spectrum shape differs from the allowedone by a factor [51]

ðW2−1Þ þ ðW0−WÞ2 ð2Þ

with W the total energy of the β particle and W0 the total endpointenergy, both in units of the electron rest mass mec2. Afterimplementing the necessary correction factors the experimentaland simulated spectra are found to agree within 2% (see Fig. 11).

5.1.3. 90YThe isotope 90Y (β endpoint energy E0¼2.2 MeV) was obtained

as the decay product of 90Sr (β endpoint energy E0¼546 keV). Onlythe decay of 90Y was simulated and simulation and experimentwere only compared in the part of the 90Y β spectrum above the90Sr β endpoint energy. As 90Y decays via a first forbidden unique βtransition the same correction factors were applied to the Geant4spectrum generator as in the case of 85Kr. The accuracy of thesimulations is rather limited for energies below 1 MeV (Fig. 12).The upper 1 MeV of the spectrum can be reproduced with ∼5%precision. Besides the fact that this is a first forbidden uniquetransition this observed difference could be in part due to the factthat the exact geometry of the source was known with much lessprecision compared to the other sources. Previous measurements[33] with 60Co have shown that the measured spectrum is indeedrather sensitive to the detailed geometry of the source.

5.1.4. 60CoThis isotope is very well suited to test the performance of the

Geant4 code for low energy β particles due to its relatively simpledecay scheme. The β endpoint energy is 318 keV which is muchlower than the energies of the two strong γ lines (1.173 and1.332 MeV) in the decay of this isotope. The problem of subtracting

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Fig. 12. Comparison between the simulated and measured 90Sr spectra for the 15/4detector. The normalization region is 1200–2000 keV. In this region χ2red ¼ 2:3 with532 degrees of freedom.

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Fig. 13. Comparison between the simulated and measured 60Co spectra for the 15/4detector. The small peak (marked “B”) at 310 keV is the double escape peak of the1332 keV γ line. The normalization region is 150–300 keV. In this region χ2red ¼ 2:8with 150 degrees of freedom.

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Fig. 11. Comparison between the simulated and measured 85Kr spectra for the 15/4detector. The normalization region is 300–600 keV. In this region χ2red ¼ 1:4 with 74degrees of freedom and simulation and experiment agree within 2%.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–22 17

the Compton background caused by these γ rays significantlycontributed to the error budget in past experiments [8].

Fig. 13 shows the upper part of the beta spectrum together withpart of the Compton background. In the “A” region (from 150 keVto 300 keV) the difference between simulation and experiment isaround 5%. At energies below 150 keV the difference becomesmuch larger. This can be due to several reasons:

�

a problem with simulating the backscattering of low energyelectrons (see Section 3), or

�

the Compton plateau not well being reproduced by the simula-tions (see Section 6.2.1).

A significant difference between simulation and experiment canbe observed in the intensity of the Compton background (region“C”), where the simulation shows a clear excess of counts. Thiseffect was observed before with Si detectors [8,33] as well.

5.2. Conclusions for HPGe detectors

The general features of all measured spectra are rather wellreproduced by the Geant4 simulations. The high energy part of theβ spectra is typically reproduced at the 2–3% level. However, the

lower half of the β spectra is typically much less well reproducedin simulations. A possible reason for this could be the inaccuracy ofthe backscattering coefficients at these energies, see Section 3.

Past evaluations of Geant4 performance in simulating spectra ofHPGe detectors were mostly carried out for large volume detectorsmostly employed for γ detection [13,52,53]. The observed accuracy ofseveral percents on the γ�peak efficiencies is slightly better thanwhat is found here.

The observed differences between the experimental and simu-lated spectra for a HPGe detector are found to be much larger thanthe small effects related to the choice of physics list, MSC modelsor of values for the Geant4 parameters. Therefore, unfortunately,no additional information on the best values of these parameterscan be obtained in this case.

6. Geant4 performance for PIPS detectors

A 1.5 mm thick, fully depleted pure PIPS detector (MSX03-1500,from Micron Semiconductor) was recently tested by our group, inpart to replace the Hamamatsu 0.5 mm thick PIN diode detectors[8,38]. The front dead layer of this detector is 100 nm thick. Theentrance window consists of a 300 nm thick Al grid with a 3%coverage. This detector is well suited for precision β spectroscopybecause the low Z values of Al and Si limit the probability forelectron backscattering from the entrance window. It is furtherable to fully stop up to 800 keV electrons.

The detector was tested in the same vacuum chamber used fortesting the HPGe detectors and again at 77 K (see Section 5 formore details). A 0.8 mm thick Cu collimator with a 9 mm diametercircular hole was mounted in front of the detector (Fig. 14).

6.1. Depletion

The spectra of 207Bi measured with the detector at roomtemperature showed signs that the detector was not fullydepleted. The conversion electron peaks were not of the expectedintensity. Indeed, the experimental ratio of the K conversionelectron lines K1063/K569 was 0.998(14), in clear disagreementwith the expected value of about 3.8, when assuming full deple-tion and taking into account the detection efficiency and back-scattering probability at the different energies. The results ofGeant4 simulations were supporting the assumption of partial

Energy (keV)200 400 600 800 1000

Cou

nts

(a. u

.)

10

102

103

104

105

Fig. 15. The 207Bi spectrum registered with the PIPS detector operating at 77 K. Thetwo main γ lines (at 569.7 keV and 1063 keV) are not visible, but their K, L and Mconversion electrons generate the two groups of peaks. The Compton edges of bothγ rays are also visible. The Kα and Kβ X-ray lines are visible at 74 keV and at 85 keV,respectively. Detector resolution (FWHM) is 4 keV at 482 keV.

Table 1Simulated ratio of the 207Bi conversion electron peaks K1063/K569 for differentdepletion layer thickness of the PIPS detector. The χ2red value shown is calculatedaccording to Eq. (1) when comparing the simulated spectra and the experimentalspectrum taken at 77 K, for the energy region between 100 and 1100 keV. Thestatistical uncertainties on the simulated peak ratios are of the order of 1‰. Theexperimental ratio is 3.78(11).

Depletion (mm) Peak ratios χ2red

1.39 3.71 23.11.43 3.83 17.11.47 3.94 13.51.50 3.98 11.5

Fig. 14. Sketch of the experimental setup used to measure 207Bi and 60Co spectrawith the PIPS detector. The detector–source distance is 71 mm. The entire setupwas positioned in a cryostat and cooled to 77 K in order to reach full detectordepletion.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–2218

depletion at room temperature, allowing to estimate the depletionthickness to be around 0.8–0.9 mm. After cooling the setup to 77 K(Fig. 15) the experimental conversion peak ratio became 3.78(11),fully consistent with the expected value and with the error beingdominated by the uncertainties of the conversion coefficients [54]. Inorder to confirm full depletion, simulations were performed forslightly different depletion layer thicknesses. The comparison of thesewith experiment is summarized in Table 1. Values for the K conver-sion peak ratio very close to the experimental one are found. The bestχ2red for the comparison of simulated and experimental spectra isobtained for depletion thicknesses of about 1.50 mm, thus confirmingthe probably full depletion. Note that it was observed that thisdetector can also be operated with no significant drop in performance

at liquid helium temperature (4 K) making it suitable for e.g. futureβ�asymmetry measurements using the low temperature nuclearorientation technique.

6.2. Comparisons with Geant4

Two spectrum measurements were performed with the PIPSdetector (at 77 K), one with 60Co, the other with 207Bi, since thesource geometry was best known for these two cases. Forsimulating the spectra for these isotopes, the vacuum chamberwith support structures as well as detailed detector and sourcedescriptions were again modeled in Geant4 version 9.5. In all casesthe Standard physics list was used.

6.2.1. 60CoA Si detector is suitable for precision β decay measurements

with 60Co since the low energy β�rays of this isotope will be fullystopped if the detector is at least 0.5 mm thick. The two gammalines at 1.173 and 1.332 MeV will not create visible peaks, althoughtheir conversion electrons do appear in the spectrum obtainedwith the 1.5 mm thick Si detector. Fig. 16 shows the experimentaland the simulated spectrum of 60Co for the PIPS detector. Thesimulations were obtained using the Standard physics list and theUrban MSC model with the default values for the simulationparameters mentioned in Section 2 (i.e. CFS¼ 1 μm, FR¼0.04,FG¼2.5 and Skin¼3).

The clear difference in the region of the spectrum dominatedby Compton events (i.e. above 320 keV) was further investigatedby positioning a 3 mm thick plastic (PVC) absorber between thedetector and the source in order to block the β rays. Keeping inmind that the PVC absorber slightly increases the Compton back-ground in both simulations and experiment, one can subtract thespectrum with absorber from the regular one by normalizing thespectra in the energy region above the β decay endpoint (i.e.between 350 and 600 keV). This procedure reduces the influenceof the Compton events to a second order effect, so that thedifference between simulation and experiment is now below 5%in the region from 50 to 318 keV and below 3% when normalizingbetween 150 and 300 keV (see Fig. 17).

6.2.2. Comparison of MSC models, physics lists andGeant4 parameters

The fact that simulated and experimental spectra agree up to3% for the case of 60Co (Fig. 17) allows comparing the effect ofdifferent types of Geant4 simulation parameters on the simulatedspectra. We therefore investigated the influence of the differentphysics lists and MSC models, as well as of the values of thedifferent simulation parameters.

Performing simulations with the different physics lists it wasfound that, similar to the backscattering coefficients, the simulated

Table 2χ2red values obtained by comparing experimental and simulated spectra of 60Co intwo different energy regions, using the Standard (Std.), Penelope (Pen.) andLivermore (Liv.) physics lists. The CFS was set to 1 μm, while the FR, FG and Skinsimulation parameters were set at their default values given in Section 2.

Region (keV) Std. Pen. Liv.

150–300 1.53 1.13 1.3150–318 7.75 7.14 7.97

Table 3

Energy (keV)

(Exp

- S

im)/E

xp

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

50 100 150 200 250 300

Energy (keV)100 120 140 160 180 200 220 240 260 280

(Exp

- S

im)/E

xp

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Fig. 17. Relative difference between simulated and experimental spectra of 60Co forthe 1.5 mm PIPS detector. The experimental and simulated results were obtained bysubtracting spectra with and without a 3 mm thick PVC absorber between thesource and the detector. Simulations used the Single Scattering model, while theother parameters were set according to Section 2, with CFS fixed at 1 μm. Panel(a) was normalized in the region between 50 and 318 keV yielding χ2red ¼ 4:1 for268 degrees of freedom. Panel (b) was normalized between 100 and 280 keV withχ2red ¼ 1:6 for 180 degrees of freedom.

Energy (keV)0 200 400 600 800 1000 1200 1400

Cou

nts

(a. u

.)

10-6

10-5

10-4

10-3

10-2

10-1

Simulation

Experiment

Fig. 16. Comparison between the simulated and measured spectra of 60Co for thePIPS detector. The β endpoint energy is 317.9 keV. The two peaks at 1162 and1320 keV are the conversion electrons of the two γ�rays at 1173.2 and 1332.5 keV,respectively. The γ peaks are estimated to be ∼20 times weaker than the conversionpeaks. The simulation was performed with the Standard physics list and the UrbanMSC model, while the simulation parameter values were set according to Section 2with CFS fixed at 1 μ m. Both spectra were normalized to the number of counts inthe energy region of 150–300 keV.

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–22 19

spectra of 60Co were not significantly influenced by the choice ofthe physics list, i.e. similar χ2red values were obtained for bothenergy regions and for all three physics lists; see Table 2. Theamount of computing time required for physics lists other than theStandard one is found to be roughly two times larger.

In simulations performed using the different MSC models theχ2red values listed in Table 3 were obtained. The Single Scatteringand the Goudsmit–Saunderson models clearly outperform theUrban MSC model, yielding a χ2red value that is up to about 50%smaller when the larger energy region from 50 to 318 keV isconsidered. The Goudsmit–Saunderson model performs similar tothe Single Scattering model, but because of the straggling in thebackscattering coefficients (see Fig. 3) it cannot be recommended.

Comparing simulations performed with different CFS valuesthe results that are summarized in Table 4 were obtained. Keepingin mind that a CFS value of 1 mm is too large when simulating theperformance of detectors which are only several mm thick, thebest value for the CFS is found to be around 10 μm to 0.1 mm, witha preference for the smaller value in view of this size issue.

Finally, simulations were performed for FR¼0.002 and for thedefault value of 0.04, resulting in χ2red ¼ 6:3 and 7.75, respectively,for the energy region of 50–318 keV. This difference being lesssignificant than the differences in χ2red obtained when varying thephysics lists, the MSC models or the CFS value we suggest to keepthe default value for FR. The FG and Skin parameters were foundnot to influence significantly the simulated spectra.

In order to investigate the accuracy of the electron processeswithin Geant4 in greater detail, experimental data for pure groundstate to ground state β transitions are required so that no Comptoneffect has to be considered.

χ2red values obtained by comparing experimental and simulated spectra of 60Co intwo different energy regions, using the Standard physics list with the Urban,Goudsmit–Saunderson (G–S) and Single Scattering (SS) MSC models. The CFS wasset to 1 μm, while the FR, FG and Skin simulation parameters were set at theirdefault values given in Section 2.

Region (keV) Urban G–S SS

150–300 1.53 1.25 1.1050–318 7.75 3.71 4.76

6.2.3. 207BiThis isotope is the most demanding for Geant4, as was already

discussed in Section 5.1. Fig. 15 shows the experimentally obtainedspectrum, while Fig. 18 shows the difference between simulationand experiment. In the region of the spectrum dominated by theX-rays (at 75 and 85 keV) the difference increases to 40%, while inthe higher energy region it is around 10%.

Energy (keV)200 400 600 800 1000

(Exp

-Sim

)/Exp

-0.4

-0.2

0

0.2

0.4

0.6

Fig. 18. Relative difference between the experimental and simulated spectrum for207Bi. Simulation parameters were set according to Section 2. The normalizationregion is from 100 to 1100 keV. The spikes visible at around 400 and 860 keV arethe differences near the Compton edges; see text and Fig. 19 for details.

Energy (keV)200 250 300 350 400

Cou

nts

(a. u

.)

0.002

0.003

0.004

0.005

0.006

0.007

Standard

Livermore

Experiment

Fig. 19. The Compton edge of the 569.7 keV γ line of 207Bi, measured using the PIPSdetector. The simulated spectra were obtained using the Standard and theLivermore physics list with the Urban MSC model.

Table 4χ2red values obtained by comparing experimental and simulated spectra of 60Co intwo different energy regions, using the Standard physics list with the Urban MSCmodel, for values of the CFS parameter ranging from 1 μm to 1 mm. The FR, FG andSkin simulation parameters were set at their default values given in Section 2.

Region (keV) 1 μm 10 μm 0.1 mm 1 mm

150–300 1.53 1.03 1.07 1.1350–318 7.75 4.83 3.09 3.28

G. Soti et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 11–2220

The most significant difference is observed in the region of theCompton plateau of the 569.7 keV γ line, i.e. the energy region upto about 400 keV. Further, the Compton edge in the simulatedspectrum is much sharper and more intense by ∼15%. Usingdifferent physics lists was found to yield slightly different results,e.g. the spectrum generated with the Livermore physics listdisplays a smoother Compton edge than the Standard one, inbetter agreement with the experimental spectrum (see Fig. 19).However, the difference in the intensity of the Compton edge isstill of the order of 10%. The Penelope physics list was found toproduce very similar results.

7. Conclusions and outlook

The influence of the various Geant4 physics lists, MSC modelsand parameters on simulated electron backscattering coefficientsfrom Si for energies in the range of nuclear β decay was investi-gated. It was found that for the energy region of typical low energyexperiments in neutron and nuclear β decay the usage of the lowenergy physics lists-Livermore and Penelope-is not absolutelyrequired. Best agreement between the simulated results andexperimental data is found for the Single Scattering model,although the other MSC models are also within the (still ratherlarge) experimental uncertainty. The default value for CFS, whichis 1 mm, should be lowered for geometrical reasons and ourrecommended value is around 10 μm. Our recommended value forthe FR parameter is in the range between 0.01 and 0.002. Highprecision experimental data on backscattering, but also on trans-mission through thin foils, in the energy range of 100 and1000 keV would be very useful for further investigation. Such aproject is currently being prepared using a β spectrometer whichcombines an energy sensitive detector and a multi-wire driftchamber similar to the one described in Refs. [55,56].

Simulations of the response of semiconductor particle detec-tors (3 mm thick HPGe and 1.5 mm thick PIPS) were also com-pared to experimental data. A general good agreement was foundfor electron processes, while for γ processes significant differenceswere observed in the region of the Compton edge. The overallworse agreement for HPGe detectors is not surprising due to thehigher Z value of Ge, since both electron and γ processes are Zdependent.

The observed good accuracy that was found for the electronprocesses in Geant4 now allows for direct precision measurementsof the β spectrum shape. For the case of a pure β emitter, with no γrays in its decay, the dominant systematic effect remaining is thebackscattering from the energy sensitive detector. Combining thenthe detector with a system that identifies backscattered events(such as the multi-wire drift chamber mentioned above [55,56])enables performing high precision measurements of the β spec-trum shape. Such experiments are currently being prepared. Thesewould allow to address the Fierz interference term that is sensitiveto scalar and tensor type components in the weak interaction [57],and to study the effect of the so-called recoil terms [58] in nuclearβ decay.

Acknowledgments

This work was supported by the Fund for Scientific ResearchFlanders (FWO), Projects GOA/2004/03 and GOA/2010/10 of theK. U. Leuven, the Interuniversity Attraction Poles Programme,Belgian State Belgian Science Policy (BriX network P6/23), andGrant LA08015 of the Ministry of Education of the Czech Republic.

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