Cosmogenic activation of silicon
R. Saldanha, R. Thomas, R.H.M. Tsang, A.E. Chavarria, R. Bunker, J.L. Burnett, S.R. Elliott, A. Matalon, P. Mitra, A. Piers, P. Privitera, K. Ramanathan, R. Smida
CCosmogenic activation of silicon
R. Saldanha, ∗ R. Thomas, R.H.M. Tsang,
1, †
A.E. Chavarria, R. Bunker, J. Burnett, S.R. Elliott, A. Matalon, P. Mitra, A. Piers, P. Privitera, K. Ramanathan, and R. Smida Pacific Northwest National Laboratory, Richland, WA 99352, USA Kavli Institute for Cosmological Physics and The Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637, USA Center for Experimental Nuclear Physics and Astrophysics, University of Washington, Seattle, Washington 98195, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
The production of H, Be, and Na by interactions of cosmic-ray particles with silicon can pro-duce radioactive backgrounds in detectors used to search for rare events. Through controlled irradi-ation of silicon CCDs and wafers with a neutron beam that mimics the cosmic-ray neutron spectrum,followed by direct counting, we determined that the production rate from cosmic-ray neutrons atsea level is (112 ±
24) atoms/(kg day) for H, (8.1 ± Be, and (43.0 ± Na. Complementing these results with the current best estimates of activa-tion cross sections for cosmic-ray particles other than neutrons, we obtain a total sea-level cosmic-ray production rate of (124 ±
24) atoms/(kg day) for H, (9.4 ± Be, and(49.6 ± Na. These measurements will help constrain background estimatesand determine the maximum time that silicon-based detectors can remain unshielded during detec-tor fabrication before cosmogenic backgrounds impact the sensitivity of next-generation rare-eventsearches.
I. INTRODUCTION
Interactions of cosmic-ray particles with detector ma-terials can produce radioactive isotopes that createbackgrounds for experiments searching for rare eventssuch as dark matter interactions and neutrinoless dou-ble beta decay. Silicon is a widely used detector mate-rial because it is available with very high purity, whichleads to low intrinsic radioactive backgrounds. In par-ticular, solid-state silicon-based detector technologiesshow promise because their eV-scale energy thresh-olds [1–3] provide sensitivity to scattering events be-tween atoms and “low-mass” dark matter particles withmasses below 1 GeV/c [4].Three prominent low-mass dark matter efforts thatemploy silicon detectors are DAMIC [5], SENSEI [1],and SuperCDMS [6]. All three use the highest-puritysingle-crystal silicon as detector substrates [7], with sen-sors fabricated on the surfaces for readout of charge orphonons and installed in low-background facilities toreduce the event rate from environmental backgrounds.A primary challenge in these rare-event searches isto distinguish potential signal events from the muchhigher rate of interactions due to conventional sourcesof radiation, both from the terrestrial environment andin the detector materials. A variety of mitigation strate-gies are used to minimize backgrounds; nevertheless,a nonzero residual background expectation is gener-ally unavoidable. Despite the high purity of silicon,the dominant residual backgrounds in future silicon-based experiments are expected to be intrinsic to and ∗ Corresponding author: [email protected] † Now at: Department of Physics and Astronomy, University of Al-abama, Tuscaloosa, Alabama 35487, USA on the surfaces of the silicon substrates. Beta-emittingradiocontaminants are especially challenging, becausethe decay products can produce energy signals that areindistinguishable from the expected dark matter signal.Both DAMIC and SuperCDMS have investigated thesedetector backgrounds (see, e.g., Refs. [6, 8, 9]), and theyhave identified H (tritium) and Si (intrinsic to the sil-icon) and
Pb (surface contamination) as the leadingsources of background for future silicon-based experi-ments. Unlike for Si, there are not yet any direct mea-surements of the tritium background in silicon; currentestimates are based on models that have yet to be vali-dated.Tritium and other radioactive isotopes such as Be and Na are produced in silicon detectors as aresult of cosmic-ray exposure, primarily due to inter-actions of high-energy cosmic-ray neutrons with sil-icon nuclei in the detector substrates [10, 11]. Thelevel of background from cosmogenic isotopes in thefinal detector is effectively determined by the above-ground exposure time during and following detec-tor production, the cosmic-ray flux, and the isotope-production cross sections. The neutron-induced pro-duction cross sections for tritium, Be, and to a lesserextent Na, are not experimentally known except fora few measurements at specific energies. There areseveral estimates of the expected cross sections; how-ever, they vary significantly, leading to large uncertain-ties in the expected cosmogenic background for rare-event searches that employ silicon detectors. To addressthis deficiency, we present measurements of the inte-grated isotope-production rates from a neutron beamat the Los Alamos Neutron Science Center (LANSCE)ICE HOUSE facility [12, 13], which has a similar en-ergy spectrum to that of cosmic-ray neutrons at sealevel. This spectral-shape similarity allows for a fairly a r X i v : . [ phy s i c s . i n s - d e t ] J u l Isotope Half-Life Decay Q-value[yrs] Mode [keV] H 12.32 ± β - 18.591 ± Be 0.1457 ± ± Be (1.51 ± × β - 556.0 ± C 5700 ± β - 156.475 ± Na 2.6018 ± β + 2842.2 ± Al (7.17 ± × EC 4004.14 ± >
30 daysthat can be produced by cosmogenic interactions with naturalsilicon. All data is taken from NNDC databases [14]. direct extrapolation from the measured beam produc-tion rates to the expected cosmogenic production rates.While the spectral shape is similar, the flux of neutronsfrom the LANSCE beam greater than 10 MeV is roughly5 × times larger than the cosmic-ray flux, whichenables production of measurable amounts of cosmo-genic isotopes in short periods of time. Our measure-ment will allow the determination of acceptable above-ground residency times for future silicon detectors, aswell as improve cosmogenic-related background esti-mates and thus sensitivity forecasts.We begin in Sec. II with a discussion of radioiso-topes that can be cosmogenically produced in silicon,and we identify those most relevant for silicon-baseddark matter searches: H, Be, and Na. For thesethree isotopes, we review previous measurements of theproduction cross sections and present the cross-sectionmodels that we use in our analysis. Section III in-troduces our experimental approach, in which severalsilicon targets—a combination of charge-coupled de-vices (CCDs) and wafers—were irradiated at LANSCE.In Sec. IV and Sec. V we present our measurementsand predictions of the beam-activated activities, respec-tively. These results are combined in Sec. VI to provideour best estimates of the production rates from cosmo-genic neutrons. In Sec. VII we evaluate other (non-neutron) production mechanisms and we conclude inSec. VIII with a summarizing discussion.
II. COSMOGENIC RADIOISOTOPES
Most silicon-based dark matter experiments usehigh-purity ( (cid:29) Si, 4.7% Si, 3.1% Si [15]) as the target detector material. Thecosmogenic isotopes of interest for these experimentsare therefore any long-lived radioisotopes that can beproduced by cosmic-ray interactions with silicon; Ta-ble I lists all isotopes with half-lives greater than 30days that are lighter than Si + n/p. None of themhave radioactive daughters that may contribute addi-tional backgrounds. Assuming that effectively all non-silicon atoms present in the raw material are drivenout during growth of the single-crystal silicon boulesused to fabricate detectors, and that the time betweencrystal growth and moving the detectors deep under-
10 Energy [MeV] -
10 110 Cross Section [mbarn] H Si(n,x) nat H Si(p,x) nat
Konobeyev & Korovin (ACTIVIA)TALYSINCL++ (ABLA 07)Geant4 INCLXXGeant4 BERTINIGeant4 BIC
FIG. 1. Experimental measurements (magenta error bars)[18–20] and model estimates (continuous curves) of neutron-induced tritium production in silicon. Measurements of theproton-induced cross section [21, 22] are also shown for refer-ence (gray error bars). ground is typically less than 10 years, cosmogenic iso-topes with half-lives greater than 100 years (i.e., Be, C, and Al) do not build up sufficient activity [16, 17]to produce significant backgrounds. Thus the cosmo-genic isotopes most relevant to silicon-based rare-eventsearches are tritium, Be, and Na. Tritium is a partic-ularly dangerous background for dark matter searchesbecause it decays by pure beta emission and its low Q-value (18.6 keV) results in a large fraction of decays thatproduce low-energy events in the expected dark mat-ter signal region. Be decays by electron capture, ei-ther directly to the ground state of Li (89.56%) or viathe 477 keV excited state of Li (10.44%). Be is not acritical background for dark matter searches, because ithas a relatively short half-life (53.22 day); however, the54.3 eV atomic de-excitation following electron captureis a potentially useful energy-calibration tool. Na de-cays primarily by positron emission (90.3%) or electroncapture (9.6%) to the 1275 keV level of Ne. For thin sil-icon detectors Na can be a significant background asit is likely that both the 1275 keV γ ray and the 511 keVpositron-annihilation photons will escape undetected,with only the emitted positron or atomic de-excitationfollowing electron capture depositing any energy in thedetector. Note that compared to H, the higher β + endpoint (546 keV) means that a smaller fraction of the Na decays produce signals in the energy range of in-terest for dark matter searches.
A. Tritium Production
Tritium production in silicon at sea-level is domi-nated by spallation interactions of high-energy cosmo-genic neutrons with silicon nuclei. Tritium is a pure β emitter and it is therefore not possible to directly mea-sure the production cross section using conventionalmethods that rely on γ -ray detectors to tag the reac-tion products. There are three previous experimentalmeasurements of the neutron-induced tritium produc-tion cross section in silicon (shown in Fig. 1), whicheither extracted tritium from a silicon target and mea-sured the activity in a proportional counter [18] or mea-sured the triton nuclei ejected from a silicon target us-ing ∆ E − E telescopes [19, 20]. The proton-inducedcross section is expected to be similar to that of neutronsso we also show previous measurements with protonbeams [21, 22]. While these measurements provide use-ful benchmarks at specific energies, they are insufficientto constrain the cosmogenic production cross sectionacross the full range of relevant neutron energies (from ∼
10 MeV to a few GeV).For this reason, previous estimates of tritium produc-tion in silicon dark matter detectors have relied on esti-mates of the cross section from calculations and simula-tions of the nuclear interactions or compiled databasesthat combine calculations with experimental data [23–25]. The production of tritons due to spallation is diffi-cult to model, because the triton is a very light nucleusthat is produced not only during the evaporation or de-excitation phase but also from coalescence of nucleonsemitted during the high-energy intra-nuclear cascadestage [26–28]. Due to large variations among the predic-tions of different cross-section models, we consider sev-eral models for comparison to our experimental resultsand extraction of cosmogenic production rates. Shownin Fig. 1 are the semi-empirical formulae of Konobeyevand Korovin (K&K) [29] (extracted from the commonlyused ACTIVIA code [30]) and results from nuclear reac-tion calculations and Monte Carlo simulations that areperformed by codes such as TALYS [31], INCL [32] andABLA [33]. We also compared effective cross sections(extracted through simulation) from built-in physics li-braries of the widely used Geant4 simulation package[38, 39] such as INCLXX [32, 36], BERTINI [40–43], andBinary Cascades (BIC) [44]. B. Be Production Be is produced as an intermediate-mass nuclearproduct of cosmogenic particle interactions with sili-con. The neutron-induced production cross section has The Konobeyev and Korovin ( H), and Silberberg and Tsao ( Be, Na) cross sections were obtained from the ACTIVIA code pack-age [34], the TALYS cross sections were calculated using TALYS-1.9 [35], and the INCL cross sections were calculated using theINCL++ code (v6.0.1) with the ABLA07 de-excitation model [36].The default parameters were used for all programs. We note thatthe TALYS models are optimized in the 1 keV to 200 MeV energyrange though the maximum energy has been formally extended to1 GeV [37]. We used Geant4.10.3.p02 with physics lists QGSP INCLXX 1.0(INCL++ v5.3), QGSP BERT 4.0, and QGSP BIC 4.0.
10 Energy [MeV] - - -
10 110 Cross Section [mbarn] Be Si(n,x) nat Be Si(p,x) nat
Be Spline Fit Si(p,x) nat
Silberberg & Tsao (ACTIVIA)TALYSINCL++ (ABLA 07)Geant4 INCLXXGeant4 BERTINIGeant4 BIC
FIG. 2. Experimental measurements (magenta error bars)[45] and model estimates (continuous curves) of the neutron-induced Be production cross section in silicon. Measure-ments of the proton-induced cross section [46, 47] are alsoshown for reference (gray error bars). been measured at only two energies [45], as shown inFig. 2. Although the neutron- and proton-induced crosssections are not necessarily the same, especially forneutron-deficient nuclides such as Be and Na [45],there are a large number of measurements with protonsthat span the entire energy range of interest [46, 47],which we show in Fig. 2 for comparison. For easeof evaluation, we fit the proton cross-section data witha continuous 4-node spline, hereafter referred to as“ nat
Si(p,x) Be Spline Fit”. As with tritium, we also showpredictions from different nuclear codes and semi-empirical calculations, including the well-known Sil-berberg and Tsao (S&T) semi-empirical equations [51–56] as implemented in the ACTIVIA code. We notethat the model predictions for the Be production crosssection in silicon vary greatly, with significantly differ-ent energy thresholds, energy dependence, and magni-tude. Be is believed to be produced predominantly asa fragmentation product rather than as an evaporationproduct or residual nucleus [49], and fragmentationis typically underestimated in most theoretical models[49, 57]. We note that unlike for the tritium cross-sectionmodels, there is a significant difference between thepredictions obtained by evaluating the INCL++ v6.0.1model directly versus simulating with Geant4 (INCL++v5.3), probably due to updates to the model. C. Na Production Na is produced as a residual nucleus following cos-mogenic interactions with silicon. Compared to tri- We have excluded measurements from Ref. [48], because there arewell-known discrepancies with other measurements [49, 50].
10 Energy [MeV] -
10 110 Cross Section [mbarn] Na Si(n,x) nat Na Si(p,x) nat
Michel (1995) - TALYSSilberberg & Tsao (ACTIVIA)TALYSINCL++ (ABLA 07)Geant4 INCLXXGeant4 BERTINIGeant4 BIC
FIG. 3. Experimental measurements (magenta error bars)[45, 58–61] and model estimates (continuous curves) of theneutron-induced Na production cross section in silicon.Measurements of the proton-induced cross section [46, 47] arealso shown for reference (gray error bars). tium and Be, the production of Na is the best stud-ied. Measurements of the neutron-induced cross sec-tion were carried out by Michel et. al. using quasi-monoenergetic neutrons between 33 and 175 MeV,with TALYS-predicted cross sections used as the ini-tial guess to unfold the experimentally measured pro-duction yields [58, 59]. These, along with six otherdata points between 66 and 370 MeV [45, 60, 61], areshown in Fig. 3. Proton-induced cross-section measure-ments [46, 47] span the entire energy range of interestand are significantly larger than the measured neutron-induced cross sections. As before, we also show the pre-dicted cross sections from Silberberg and Tsao, TALYS,INCL++ (ABLA07) and Geant4 models. In order tocompare the existing neutron cross-section measure-ments to our data, we use a piecewise model that fol-lows the measurements in Refs. [58, 59] below 180 MeVand follows the TALYS model at higher energies. Thismodel is hereafter referred to as “Michel-TALYS” (seeFig. 3). Na can also be produced indirectly throughthe production of the short-lived isotopes Mg, Al,and Si, which eventually decay to Na, but for themodels considered the total contribution from these iso-topes is < III. BEAM EXPOSURE
To evaluate the production rate of cosmogenic iso-topes through the interaction of high-energy neutrons,we irradiated silicon charge-coupled devices (CCDs)and silicon wafers at the LANSCE neutron beam fa-cility. Following the irradiation, the CCDs were read-out to measure the beam-induced β activity within the Similar to Be, we have excluded measurements from Ref. [48].
CCD active region, and the γ activity induced in thewafers was measured using γ -ray spectroscopy. In thissection we describe the details of the targets and beamexposure, while in Sec. IV we present the measurementresults. A. CCDs
The irradiated CCDs were designed and procured byLawrence Berkeley National Laboratory (LBNL) [62] forthe DAMIC Collaboration. CCDs from the same fabri-cation lot were extensively characterized in the labora-tory and deployed underground at SNOLAB to searchfor dark matter [3]. The devices are three-phase sci-entific CCDs with a buried p -channel fabricated on a670 µm-thick n -type high-resistivity (10–20 k Ω cm) sili-con substrate, which can be fully depleted by apply-ing >
40 V to a thin backside contact. The CCDs fea-ture a 61.44 × rectangular array of 4096 × ×
15 µm ) and an active thickness of ( ± ) µm. By mass, the devices are >
99 % ele-mental silicon with natural isotopic abundances. Otherelements present are oxygen ( ∼ < < β particle will produceon average one electron-hole pair for every 3.8 eV of de-posited energy. The ionization charge is drifted by theapplied electric field and collected on the pixel array.The CCDs are read out serially by moving the chargevertically row-by-row into the serial register (the bot-tom row) where the charge is moved horizontally pixel-by-pixel to the output readout node. Before irradiation,the charge-transfer inefficiency from pixel to pixel was < − [62], the dark current was < − /pixel/h, andthe uncertainty in the measurement of the charge col-lected by a pixel was ∼ e − RMS. Further details onthe response of DAMIC CCDs can be found in Sec. IVof Ref. [3]. Even after the significant increase in CCDnoise following irradiation (e.g., due to shot noise asso-ciated with an increase in dark current), the CCD canstill resolve most of the tritium β -decay spectrum.Irradiation generates defects in silicon devices thatcan trap charges and negatively impact the perfor-mance of CCDs. Fully-depleted devices are resilientto irradiation damage in the bulk silicon because theionization charge is collected over a short period oftime, which minimizes the probability of charge beingtrapped by defects before it is collected. For this rea-son LBNL CCDs have been considered for space-basedimaging where the devices are subjected to high levelsof cosmic radiation [63]. Measurements at the LBNLcyclotron demonstrated the remarkable radiation tol-erance of the CCDs proposed for the SNAP satellite,which follow the same design principles and fabrica-tion process as the DAMIC CCDs. For the measure-ments presented in this paper, there is a trade-off be-tween activation rate and CCD performance. Higherirradiation leads to a higher activity of radioisotopesin the CCD and hence a lower statistical uncertainty inthe measurement. On the other hand, higher irradiationalso decreases the CCD performance, which needs to bemodeled and can thus introduce significant systematicuncertainty.The two most relevant performance parameters af-fected by the irradiation are the charge-transfer ineffi-ciency (CTI) and the pixel dark current (DC). Ref. [63]provides measurements of CTI and DC after irra-diation with 12.5 and 55 MeV protons. Followingirradiation doses roughly equivalent to a LANSCEbeam fluence of 2.4 × neutrons above 10 MeV, theCCDs were still functional with the CTI worsened to ∼ − and asymptotic DC rates (after days of oper-ation following a room-temperature anneal) increasedto ∼
100 e − /pixel/h. These values depend strongly onthe specific CCD design and the operation parameters,most notably the operating temperature. Consideringthe available beam time, the range of estimated pro-duction rates for the isotopes of interest, and the CCDbackground rates, we decided to irradiate three CCDswith different levels of exposure, roughly correspond-ing to 2.4 × , 1.6 × , and 0.8 × neutronsabove 10 MeV at the LANSCE neutron beam. Further-more, we used a collimator (see Sec. III C) to suppressirradiation of the serial register at the edge of the CCDsby one order of magnitude and thus mitigate CTI in thehorizontal readout direction.The CCDs were packaged at the University of Wash-ington following the procedure developed for theDAMIC experiment. The CCD die and a flex cable wereglued onto a silicon support piece such that the electri-cal contact pads for the signal lines are aligned. TheCCDs were then wedge bonded to the flex cable with25 µm-thick aluminum wire. A connector on the tailof the flex cable can be connected to the electronics fordevice control and readout.Each packaged device was fixed inside an aluminumstorage box, as shown in Fig. 4. The CCDs were keptinside their storage boxes during irradiation to preservethe integrity of the CCD package, in particular to pre-vent the wire bonds from breaking during handlingand to reduce any possibility of electrostatic discharge,which can damage the low-capacitance CCD microelec-tronics. To minimize the attenuation of neutrons alongthe beam path and activation of the storage box, thefront and back covers that protect each CCD were madefrom relatively thin (0.5 mm) high-purity aluminum (al-loy 1100). B. Wafers
In addition to the CCDs, we exposed several Siwafers, a Ge wafer, and two Cu plates to the neutron
FIG. 4. Photograph of the CCD package inside its aluminumstorage box. Left: Package before wire bonding. Right: Afterwire bonding, with aluminum frame to keep the CCD pack-age fixed in place. beam. These samples served both as direct targets foractivation and measurement of specific radioisotopes,and as witness samples of the neutron beam. In thispaper, we focus on the Si wafers; however, the Ge waferand Cu plates were also measured and may be the sub-ject of future studies.A total of eight Si wafers (4 pairs) were used: onepair matched to each of the three CCDs (such that theyhad the same beam exposure time) and a fourth pairthat served as a control sample. The eight wafers werepurchased together and have effectively identical prop-erties. Each wafer was sliced from a Czochralski-grownsingle-crystal boule with a 100-mm diameter and a re-sistivity of > Ω cm. The wafers are undoped, werepolished on one side, and have a (cid:104) (cid:105) crystal-planealignment. The thickness of each individual wafer is ( ± ) µm (based on information from the vendor).The control sample was not exposed to the neutronbeam and thus provides a background reference forthe gamma counting. Note that because the waferswere deployed and counted in pairs, henceforth wedistinguish and refer to only pairs of wafers ratherthan individual wafers. The (single) Ge wafer is also100 mm in diameter and undoped, with a thickness of ( ± ) µm, while the Cu plates have dimensions of114.7 × × C. LANSCE Beam Exposure
The samples were irradiated at the LANSCE WNRICE-HOUSE II facility [13] on Target 4 Flight Path 30Right (4FP30R). A broad-spectrum (0.2–800 MeV) neu-tron beam was produced via spallation of 800 MeV pro-tons on a tungsten target. A 2.54-cm (1”) diameter beamcollimator was used to restrict the majority of the neu-trons to within the active region of the CCD and thusprevent unwanted irradiation of the serial registers onthe perimeter of the active region. The neutron flu-ence was measured with
U foils by an in-beam fis-sion chamber [64] placed downstream of the collimator.The beam has a pulsed time structure, which allowsthe incident neutron energies to be determined usingthe time-of-flight technique (TOF)—via a measurementbetween the proton beam pulse and the fission chambersignals [12, 64].The beam exposure took place over four days be-tween September 18 th and 22 nd , 2018. On Sept. 18,CCD 1 was placed in the beam line at 18:03 local time,located closest to the fission chamber, along with a pairof Si wafers, one Ge wafer, and one Cu plate placeddownstream (in that order; cf. Fig. 5 left). The frontface of the Al box containing CCD 1 was 260 mm fromthe face of the fission chamber. At 17:16 on Sept. 20,CCD 2 was added directly downstream from CCD 1,along with another pair of Si wafers. The front face ofthe Al box for CCD 2 was 14.3 mm from the front face ofCCD 1. At 09:11 on Sept. 22, CCD 3 was added down-stream with an equidistant spacing relative to the otherCCDs, along with another pair of Si wafers and a sec-ond Cu plate. Figure 5 shows schematics of these threeexposure setups, while Fig. 6 shows a photograph of thefinal setup in which all three CCDs were on the beamline. The exposure was stopped at 08:00 on Sept. 23,and all parts exposed to the beam were kept in stor-age for approximately seven weeks to allow short-livedradioactivity to decay prior to shipment for counting. D. Target Fluence
The fluence measured by the fission chamber duringthe entire beam exposure is shown in Fig. 7, with a to-tal of ( ± ) × neutrons above 10 MeV. Theuncertainty is dominated by the systematic uncertaintyin the U(n, f) cross section used to monitor the flu-ence, shown in Fig. 8. Below 200 MeV the assumedLANSCE cross section and various other experimentalmeasurements and evaluations [65–67] agree to betterthan 5%. Between 200 and 300 MeV there are only twomeasurements of the cross section [65, 68] which differby 5–10%. Above 300 MeV there are no experimentalmeasurements. The cross section used by the LANSCEfacility assumes a constant cross section above 380 MeVat roughly the same value as that measured at 300 MeV[68]. This is in tension with evaluations based on ex-trapolations from the
U(p, f) cross section that rec-ommend an increasing cross section to a constant valueof roughly 1.5 b at 1 GeV [69, 70]. We have used theLANSCE cross section and assumed a 5% systematicuncertainty below 200 MeV, a 10% uncertainty between200 and 300 MeV, and a constant 20% uncertainty be-tween 300 and 750 MeV. The uncertainty in the neutronenergy spectrum due to the timing uncertainty in theTOF measurement (1.2 nsec) is negligible for this mea-surement.While the nominal beam diameter was set by the 1”collimator, the cross-sectional beam profile has signif-icant tails at larger radii. At the fission chamber ap-proximately 38.8% of neutrons fall outside a 1” diam-eter, as calculated with the beam profile provided by
Target Exposure Time Neutrons through target[hrs] ( >
10 MeV)CCD 1 109.4 ( ± ) × Wafer 1 109.4 ( ± ) × CCD 2 62.7 ( ± ) × Wafer 2 62.7 ( ± ) × CCD 3 22.8 ( ± ) × Wafer 3 22.8 ( ± ) × TABLE II. Beam exposure details for each CCD and its Si-wafer matched pair.
LANSCE. Additionally the beam is slightly diverging,with an estimated cone opening angle of 0.233 ◦ . AGeant4 [38, 39] simulation that included the measuredbeam profile and beam divergence, the measured neu-tron spectrum, and the full geometry and materials ofthe targets, mounting apparatus, and fission chamber,was used to calculate the neutron fluence through eachmaterial, accounting for any attenuation of the neutronsthrough the targets. To reduce computational time, a bi-asing technique was used to generate neutrons. Insteadof following the beam profile, neutrons were generateduniformly in a 16 cm ×
16 cm square in front of the fis-sion chamber, covering the entire cross-sectional area ofthe setup. After running the Geant4 simulation, eachevent was assigned a weight which is proportional tothe intensity of the beam at the simulated neutron loca-tion, as obtained from the two-dimensional beam pro-file supplied by LANSCE. This allows reuse of the samesimulation results for different beam profiles and align-ment offsets. A total of 5.5 × neutrons above 10MeV were simulated for each setup and physics list. Atthis level of statistics, the statistical uncertainties in thesimulation are sub-dominant to the total neutron flu-ence uncertainty.The simulations show that each CCD receives about83 % of the whole beam. To assess the uncertainty inthe neutron fluence due to misalignment of the beamwith the center of the CCDs, the profile of the beamwas reconstructed by measuring the dark current ratein the CCDs as a function of position (see Sec. IV B). Thebeam misalignment is calculated to be about − x direction and + y direction, whichwhen input into the Geant4 simulation yields a sys-tematic uncertainty in the neutron fluence of less than1%. The total neutron fluence ( >
10 MeV) through eachCCD and its Si-wafer matched pair is listed in Table II;corresponding energy spectra are shown in Fig. 7 (thespectral shape of the fluence through each Si-wafer pairis very similar to that of the corresponding CCD andhas been omitted for clarity).
FIG. 5. Geant4 renderings of the three setups used to position targets in the neutron beam, with the beam passing from right toleft. Aluminum (Al) boxes holding the CCDs (yellow) were held in place by an Al rack (dark gray). For the initial setup (left),the Al box is made transparent to show the positioning of the CCD (red), air (grey), and other structures (light brown). Theother targets include pairs of Si wafers (green), a Ge wafer (blue), and Cu plates (copper brown). The polyethylene wafer holder(purple) is simplified to a rectangle of the same thickness and height as the actual object, with the sides and bottom removed.All targets were supported on an acetal block (light gray).Wafer 0 Wafer 1 Wafer 2 Wafer 3Si areal density [atoms/cm ] ( ± ) × Beam to meas. time [days] - 184.107 187.131 82.342Ge counting time [days] 7.000 1.055 3.005 7.000Measured Be activity [mBq] <
40 161 ±
24 75 ±
12 149 ± Be activity [mBq] - 1830 ±
270 870 ±
140 437 ± Be cross section [cm ] - ( ± ) × − ( ± ) × − ( ± ) × − Measured Na activity [mBq] < ±
29 370 ±
16 139.5 ± Na activity [mBq] - 694 ±
33 424 ±
19 148.2 ± Na cross section [cm ] - ( ± ) × − ( ± ) × − ( ± ) × − TABLE III. Gamma-counting results for the Si-wafer pairs. Measured activities are corrected for isotope decay that occurredduring the beam exposure, as well as between the end of the beam exposure and the time of the gamma counting. Upper limitsquoted for the unirradiated pair (“Wafer 0”) represent the spectrometer’s minimum detectable activity (Currie MDA with a 5%confidence factor [72]) at the corresponding peak energy.
IV. COUNTINGA. Wafers
The gamma-ray activities of the Si-wafer pairs (in-cluding the unirradiated pair) were measured with alow-background counter at Pacific Northwest NationalLaboratory (PNNL). Measurements were performed us-ing a Canberra Broad Energy Ge (BEGe) gamma-rayspectrometer (model BE6530) situated within the shal-low underground laboratory (SUL) at PNNL [73]. TheSUL is designed for low-background measurements,with a calculated depth of 30 m water equivalent, whichresults in approximately 100 × fewer fast neutrons and6 × fewer muons. The BEGe spectrometer is optimizedfor the measurement of fission and activation products,combining the spectral advantages of low-energy andcoaxial detectors, with an energy range from 3 keV to3 MeV. The detector is situated within a lead shield(200 mm), lined with tin (1 mm) and copper (1 mm). It is equipped with a plastic scintillator counter [74–77] to veto cosmic rays, which improves sensitivityby further reducing the cosmic-induced detector back-ground by 25%. The detector was operated with a Can-berra Lynx MCA to provide advanced time-stamped listmode functionality.Each wafer pair was measured independently, withwafer pair 3 and the unexposed wafer pair 0 countedfor longer periods because their expected activities werethe lowest. Table III shows the gamma-counting de-tails, and Fig. 9 shows the measured gamma-ray spec-tra. Spectral analysis was performed using the Can-berra Genie 2000 Gamma Acquisition & Analysis soft-ware (version 3.4) and all nuclear data were takenfrom the Evaluated Nuclear Data File (ENDF) database[78] hosted at the National Nuclear Data Center byBrookhaven National Laboratory. Compared to theunirradiated wafer-pair spectrum, the only new peaksidentified in the spectra of the irradiated wafer pairs areat 478 and 1275 keV, corresponding to Be (10.44%) and
FIG. 6. Layout of the samples as placed in the beam during thefinal irradiation setup (cf. Fig. 5 right). The beam first passesthrough the cylindrical fission chamber (far right) and thenthrough the samples (from right to left): 3 CCDs in Al boxes(with flex cables emerging at the top), 3 pairs of Si wafers,1 Ge wafer, and 2 Cu plates. LANSCE 4FP30R Neutron Beam [n/MeV] - - - - - - - sec MeV)] Cosmic Neutron Flux [n/(cm
Total Beam Neutron FluenceCCD 1 Neutron FluenceCCD 2 Neutron FluenceCCD 3 Neutron FluenceCosmogenic Neutron Flux
FIG. 7. Comparison of the LANSCE 4FP30R/ICE II neu-tron beam with sea-level cosmic-ray neutrons. The black datapoints and left vertical axis show the number of neutrons mea-sured by the fission chamber during the entire beam exposureused for this measurement. Uncertainties shown are statisticalonly (see main text for discussion of systematic uncertainties).The colored markers show the simulated fluence for each ofthe CCDs in the setup. For comparison, the red continuousline and the right vertical axis show the reference cosmic-rayneutron flux at sea level for New York City during the mid-point of solar modulation [71]. Na (99.94%), respectively (cf. Fig. 9). Note that each ofthe irradiated wafer pairs also has a significant excessat 511 keV, corresponding to positron-annihilation pho-tons from Na decays, and an associated sum peak at1786 keV ( = + Be and Na activities in each wafer pair werecalculated using the 478 and 1275 keV peaks, respec-
10 Energy [MeV]0.80.91.01.11.21.31.41.51.61.71.8
Cross Section [barns]
Lisowski 1991Tovesson 2014Miller 2015IAEA Evaluation 2015Duran Evaluation 2017LANSCE
FIG. 8. Experimental measurements (circles) [65, 67, 68] andevaluations (squares) [66, 69, 70] of the
U(n, f) cross section.The cross section assumed by the LANSCE facility to convertthe fission chamber counts to a total neutron fluence is shownby the black line, with the shaded grey band indicating theassumed uncertainty. tively. The measured values listed in Table III includethe detector efficiency and true-coincidence summingcorrections for the sample geometry and gamma-rayenergies considered (calculated using the Canberra InSitu Object Counting Systems, or ISOCS, calibrationsoftware [79]). The activity uncertainties listed in Ta-ble III include both the statistical and systematic contri-butions, with the latter dominated by uncertainty in theefficiency calibration ( ∼ Be and Na (even if the com-mon systematic uncertainty associated with the neu-tron beam fluence is ignored), which serves as a cross-check of the neutron-beam exposure calculations. Thelack of any other identified peaks confirms that thereare no other significant long-lived gamma-emitting iso-topes produced by high-energy neutron interactions insilicon. Specifically, the lack of an identifiable peak at1808.7 keV allows us to place an upper limit on the pro-duced activity of Al at the minimum detectable activ-ity level of 12 mBq (Currie MDA with a 5% confidencefactor [72]), i.e. at least 58 × lower than the Na activityin wafer pair 1.
200 400 600 800 1000 1200 1400 1600 1800 2000 Energy [keV]110 Counts [counts/(day 1.6 keV)]
Si Wafer 0 (not irradiated)Si Wafer 1Si Wafer 2Si Wafer 3
460 480 500 520 540 Energy [keV]10 Counts [counts/(day 0.4 keV)] Counts [counts/(day 0.4 keV)]
FIG. 9. Spectral comparison of the gamma-counting results for the Si-wafer pairs. Inspection of the full energy range (top panel)reveals two peaks in the irradiated samples (1, 2, and 3) at 478 keV (bottom left) and 1275 keV (bottom right) that are not presentin the unirradiated sample (0), corresponding to Be and Na activated by the LANSCE neutron beam, respectively.
B. CCDs
CCD images were acquired at The University ofChicago in a custom vacuum chamber. Prior to count-ing, the CCDs were removed from the aluminum trans-port boxes and placed in a copper box inside the vac-uum chamber. Images taken were 4200 columns by 2100rows in size, with 52 rows and 104 columns constitutingthe “overscan” (i.e., empty pixel reads past the end ofthe CCD pixel array). These overscan pixels contain nocharge and thus provide a direct measurement of thepixel readout noise. Each post-irradiation image corre-sponds to a total exposure of 417 sec. A total of 8030images were acquired with CCD 3, 6174 with CCD 2,and 3875 with CCD 1, for total counting times of 38.76,30.56, and 19.79 days, respectively. Data were taken inlong continuous runs of many images. Interruptionsin data taking for testing of the CCD demarcate sepa-rate data runs for each CCD. No significant differencebetween runs was noticed and all runs for each CCDwere analyzed together.Background data for each CCD were taken prior to shipment to the LANSCE facility for neutron irradia-tion. These background data consist of the combinedspectrum from all radioactive backgrounds in the lab-oratory environment, including the vacuum chamber,the intrinsic contamination in the CCD, and cosmicrays. All data were acquired using the same readoutsettings, but a longer total exposure of 913 sec was usedfor background images. The measured backgroundspectra for the three CCDs are consistent to within sta-tistical uncertainty; so we used the largest data set ac-quired with CCD 3 for the analysis. This set contained1236 images, for a total counting time of 13.06 days.CCD images were processed with the standardDAMIC analysis software [3], which subtracts the im-age pedestal, generates a “mask” to exclude repeatingcharge patterns in the images caused by defects, andgroups pixels into clusters that correspond to individ-ual ionization events. The high dark current caused bydamage to the CCD from the irradiation (see Fig. 10)necessitated a modification to this masking procedurebecause the average CCD pixel values were no longeruniform across the entire CCD, as they were before0
Row
Dark Current [A.U.]
FIG. 10. Post-irradiation dark-current profile for CCD 3, ob-tained from the median pixel values across multiple images.The elevated number of dark counts in the center of the CCDshows the effect of the neutron damage on the CCD. irradiation. The images were therefore split into 20-column segments which were treated separately for thepedestal subtraction and masking steps.Simulations of H, Na, and Be decays in the bulksilicon of the CCD were performed using a customGeant4 simulation, using the Penelope Geant4 physicslist, with a simplified geometry that included only theCCD and the surrounding copper box. Radioactive-decay events were simulated according to the beam pro-file, assumed to be proportional to the dark current pro-file (shown in Fig. 10). The CCD response was simu-lated for every ionization event, including the stochasticprocesses of charge generation and transport that werevalidated in Ref. [80].To include the effects of noise and dark current on theclustering algorithm, simulated “blank” images werecreated with the same noise and dark-current profileas the post-irradiation data. The simulated ionizationevents were pixelated and added onto the blank images,which were then processed with the standard DAMICreconstruction code to identify clusters. The increasein the vertical (row-to-row) charge transfer inefficiency(CTI) observed in the post-irradiation data was simu-lated with a Poissonian kernel, which assumes a con-stant mean probability, λ , of charge loss for each pixeltransfer along a column [81]. We assume a dependenceof λ as a function of column number that is propor-tional to the dark current profile. The total effect of CTIon a particular cluster depends on the number of ver-tical charge transfers n . The continuous CCD readoutscheme, chosen to optimize the noise while minimizingoverlap of charge clusters, results in a loss of informa-tion about the true number of vertical charge transfersfor each cluster. For every simulated cluster we there-fore pick a random n uniformly from 1 to 2000 to sim-ulate events distributed from the bottom row to the toprow of the CCD and apply the Poissonian kernel. Wedetermined the maximum value of λ near the center ofthe CCD to be 9 × − by matching the distribution ofthe vertical spread of clusters in the simulation to thedata.For CCD 1 and CCD 2, which experienced signifi-cantly higher neutron irradiation than CCD 3, the ver- tical CTI could not be well-described with a Poisso-nian kernel. We suspect that the CTI in these CCDsis dominated by the effect of charge traps introducedby the neutron irradiation. During the readout proce-dure these traps are filled with charge from ionizationclusters. The charge is then released on the timescale ofmilliseconds, corresponding to ∼
25 vertical transfers.This effect is difficult to model and results in consid-erable loss of charge from clusters in these two CCDs.We have therefore not used CCD 1 and CCD 2 for anymeasurements and only report results from CCD 3.The identified clusters in the background data ac-quired prior to irradiation at LANSCE were also intro-duced on simulated blank images to include the effectof dark current, defects, and CTI on the backgroundspectrum in the activated region of the CCD.The post-irradiation energy spectrum measured withCCD 3 was fit using a model that includes componentsfor the CCD background, Na decays, and H decays. Be was excluded from the fit because the decay doesnot produce a significant contribution to the total en-ergy spectrum, even at many times the activity expectedfrom the wafer measurement.We constructed a binned Poissonian log-likelihood asthe test statistic for the fit, which was minimized us-ing Minuit [82] to find the best-fit parameters. Dueto the relatively low statistics in the background tem-plate compared to post-irradiation data, statistical er-rors were corrected using a modified Barlow-Beestonmethod [83], allowing each bin of the model to fluctuateby a Gaussian-constrained term with a standard devia-tion proportional to the bin statistical uncertainty. Thedata spectrum was fit from 2 to 25 keV to contain mostof the H spectrum, while excluding clusters from noiseat low energies. A 2 keV-wide energy region around thecopper K-shell fluorescence line at 8 keV was maskedfrom the fit because it is not well-modeled in the sim-ulation. This peak-like feature is more sensitive to thedetails of the energy response than the smooth H spec-trum. We have verified that including this K-shell linein the fit has a negligible effect on the fitted H activ-ity. The background rate for the fit was fixed to thepre-irradiation value, while keeping the amplitude ofthe Na spectrum free. This choice has a negligibleimpact on the H result because the background and Na spectra are highly degenerate within the fit energyrange, with a correlation coefficient of 0.993. Figure 11shows the measured energy spectrum and the best-fitresult ( χ /NDF=104/87).After the fit was performed, the activities were cal-culated by dividing the fitted counts by the cumula-tive data exposure. This number was corrected forthe isotope-specific event detection efficiency obtainedfrom the simulation for the energy region of interest.Systematic errors were estimated from a series of fitsunder different configurations, including varying theenergy range of the fit, varying the energy response1 Energy [keV]5 10 15 20 25 30
Counts [counts/ (day 0.23 keV)]
Data (CCD H Masked Region
FIG. 11. Data spectrum and best-fit model with the spectralcomponents stacked in different colors. The spectrum wasfit from 2 to 25 keV with the shaded region around the 8 keVcopper K-shell fluorescence line excluded from the fit. Therise in the spectrum below 18 keV from H decay is clearlyvisible above the nearly flat background and Na spectrum. and charge transfer parameters within their uncertain-ties, and floating versus constraining the amplitudes ofthe background and/or Na components in the fit. Thebest estimate for the tritium activity in CCD 3 (after cor-recting for radioactive decay) is 45.7 ± ± Na measurement in the CCDsis limited because the relatively flat Na spectrum isdegenerate with the shape of the background spec-trum. Unfortunately, there are no features in the CCDspectrum at low energies that can further constrain the Na activity. Further, the damage to the CCD ren-ders the spectrum at higher energies unreliable be-cause events with energies >
50 keV create large ex-tended tracks where the effects of CTI, dark current,and pileup with defects becomes considerable, prevent-ing reliable energy reconstruction. Notably, character-istic full-absorption γ lines are not present in the CCDspectrum because γ rays do not deposit their full en-ergy in the relatively thin CCDs. As a cross-checkof the post-irradiation background rate, we separatelyfit the first and last 400 columns of the CCD (a re-gion mostly free of neutron exposure) and found val-ues consistent with the pre-irradiation background towithin ∼ Na activity, which dominates the overall sys-tematic uncertainty. The best estimate for the Na ac-tivity in CCD 3 is 126 ± ±
26 (syst) mBq. Thisis consistent with the more precise measurement of the Na activity in the silicon wafers, which correspondsto a CCD 3 activity of ( ± ) mBq. Box Al CCD Si Box Al(a)(b)(c)
FIG. 12. Schematic diagram showing triton ejection and im-plantation. The filled circles indicate example triton produc-tion locations while the triton nuclei show the final implanta-tion locations. Production rate estimates include trajectories(a) and (b), while counting the tritium decay activity in theCCD measures (a) and (c).
V. PREDICTED BEAM PRODUCTION RATE
If the neutron beam had an energy spectrum iden-tical to that of cosmic-ray neutrons, we could simplyestimate the cosmogenic production rate by scaling themeasured activity by the ratio of the cosmic-ray neu-trons to that of the neutron beam. However the beamspectrum falls off faster at higher energies than that ofcosmic rays (see Fig. 7). Thus we must rely on a modelfor the production cross sections to extrapolate from thebeam measurement to the cosmogenic production rate.We can evaluate the accuracy of the different cross-section models by comparing the predicted H, Be, and Na activity produced by the LANSCE neutron beamirradiation to the decay-corrected measured activities.For a given model of the isotope production cross sec-tion σ ( E ) [cm ], the predicted isotope activity, P [Bq],produced by the beam (correcting for decays) is givenby P = n a τ (cid:90) S ( E ) · σ ( E ) dE (1)where n a is the areal number density of the target sili-con atoms [atoms/cm ], τ is the mean life [sec] of theisotope decay, and S ( E ) is the energy spectrum of neu-trons [neutrons/MeV]. The second column of Table IVshows the predicted activity in CCD 3, P CCD , for thedifferent H cross-section models considered. The cor-responding numbers for Be and Na in Wafer 3 ( P W ) are shown in Tables V and VI respectively. The uncer-tainties listed include the energy-dependent uncertain-ties in the LANSCE neutron beam spectrum and theuncertainty in the target thickness. A. Ejection and Implantation
Light nuclei, such as tritons, can be produced withsignificant fractions of the neutron kinetic energy. Due2
Model Pred. LANSCE Ejected Implanted Pred. LANSCE Meas./Pred. H prod. act. Activity Activity H res. act. H res. act. P CCD [mBq] E CCD [mBq] I CCD [mBq] R CCD [mBq]K&K (ACTIVIA) 40.8 ± ± ± ±
16 46.70 ± ± ±
17 0.370 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± H activity in CCD 3 based on different cross-section models. The second column lists the total activityproduced in the CCD, while the third and fourth columns list the activity ejected and implanted respectively. The fifth columnshows the final residual activity calculated from the second, third, and fourth columns. For models without ejection andimplantation information we use the average of the other models—see text for details. The final column shows the ratio of theexperimentally measured activity to the predicted residual activity.Model Pred. LANSCE Ejected Implanted Pred. LANSCE Meas./Pred. Be prod. act. Activity Activity Be res. act. Be res. act. P W [mBq] E W [mBq] I W [mBq] R W [mBq]S&T (ACTIVIA) 408 ±
44 405 ±
47 1.08 ± ±
39 292 ±
41 1.50 ± ±
21 140 ±
22 3.12 ± nat Si(p,x) Be Spline Fit 518 ±
66 514 ±
70 0.85 ± ± < ± ± ± ± < ± ± ± ± ± ± ± ± Be activity in Wafer 3 based on different cross-section models. See Table IV caption for a description of thecolumns. Upper limits are 90% C.L.Model Pred. LANSCE Ejected Implanted Pred. LANSCE Meas./Pred. Na prod. act. Activity Activity Na res. act. Na res. act. P W [mBq] E W [mBq] I W [mBq] R W [mBq]S&T (ACTIVIA) 295 ±
28 295 ±
28 0.502 ± ±
17 208 ±
17 0.711 ± ±
21 206 ±
21 0.718 ± ±
14 151 ±
14 0.98 ± ± < < ±
10 1.54 ± ± < < ±
39 0.378 ± ± < < ±
39 0.373 ± Na activity in Wafer 3 based on different cross-section models. See Table IV caption for a description ofthe details. Upper limits are 90% C.L. to their small mass, these nuclei have relatively longranges and can therefore be ejected from their volumeof creation and implanted into another volume. Thesituation is shown schematically in Fig. 12. While wewould like to estimate the total production rate in thesilicon targets, what is actually measured is a combi-nation of the nuclei produced in the target that are notejected and nuclei produced in surrounding materialthat are implanted in the silicon target. The measuredactivity therefore depends not only on the thickness ofthe target but also on the nature and geometry of thesurrounding materials.The residual activity, R i , eventually measured in vol-ume i , can be written as R i = ∑ j T ij · P j (2) where P j is the total activity produced in volume j (seeEq. 1) and T ij is the transfer probability—the probabilityof a triton produced in j to be eventually implanted in i . Because the ejection and implantation of light nucleiis also an issue for dark matter detectors during fabri-cation and transportation, we have also explicitly fac-tored the transfer probability into ejected activity ( E i )and activity implanted from other materials ( I i ) to givethe reader an idea of the relative magnitudes of the twocompeting effects: E i = ( − T ii ) · P i (3) I i = ∑ j (cid:54) = i T ij · P j (4) R i = P i − E i + I i (5)3
98 0 47 1 0 13 59 0 9 29 0 0 00 1 21 1 4 10 0 036 1 0 693 9 0 2 0 2111 22 0 61 414 3 2 0 0 32 4 8 6 22 151 1 0 0 0 14 4 2 14 14 9 187 5 0 4 71 2 1 2 5 3 29 111 2 5 20 0 1 0 1 2 3 11 40 4 11 1 0 3 2 1 17 16 9 183 520 12 4 91 50 19 42 21 6 41 1653
CCD1CCD2CCD3Box1Box2Box3Si1 Si2 Si3 Ge World
Produced
CCD1CCD2CCD3Box1Box2Box3Si1Si2Si3GeWorld
Implanted H
47 12 00 29 1 70 0 10 0 312 217 0 101 7 9 131 0 10 2 3 48 01 0 0 4 5 3 86 70 0 9 54 20 0 3 18 0 00 0 0 5 5 3 52 40 0 0 3 2 0 1 1 0 1 2835
CCD1CCD2CCD3Box1Box2Box3Si1 Si2 Si3 Ge World
Produced
CCD1CCD2CCD3Box1Box2Box3Si1Si2Si3GeWorld
Implanted Be CCD1CCD2CCD3Box1Box2Box3Si1 Si2 Si3 Ge World
Produced
CCD1CCD2CCD3Box1Box2Box3Si1Si2Si3GeWorld
Implanted - - mBq Na FIG. 13. Shown are the activities [mBq] of H (left), Be (middle), and Na (right) produced and implanted in various volumes(i.e., T ij · P j ) as predicted by the GEANT4 INCLXX model. CCD 1, CCD 2, CCD 3 are the CCDs, with CCD 1 being closest to thefission chamber. Box 1, Box 2, and Box 3 are the aluminum boxes that contain CCD 1, CCD 2, and CCD 3, respectively. Si 1, Si 2,Si 3, and Ge are the silicon and germanium wafers downstream of the CCDs. World represents the air in the irradiation room. For nuclear models that are built-in as physics listswithin Geant4, explicit calculations of transfer proba-bilities are not necessary, because the nuclei producedthroughout the setup are propagated by Geant4 as partof the simulation. For the TALYS model, which doescalculate the kinematic distributions for light nucleisuch as tritons but is not included in Geant4, we had toinclude the propagation of the nuclei separately. Sincethe passage of nuclei through matter in the relevantenergy range is dominated by electromagnetic inter-actions, which are independent of nuclear productionmodels and can be reliably calculated by Geant4, weused TALYS to evaluate the initial kinetic energy andangular distributions of triton nuclei produced by theLANSCE neutron beam and then ran the Geant4 simu-lation starting with nuclei whose momenta are drawnfrom the TALYS-produced distributions. For the re-maining models which do not predict kinematic distri-butions of the resulting nuclei, we simply used the aver-age and standard deviation of the transfer probabilitiesfrom the models that do provide this information. Asan example, the transfer matrix (expressed in terms ofactivity T (cid:48) ij = T ij · P j ) from the Geant4 INCLXX modelfor all three isotopes of interest is shown in Fig. 13. Theuncertainties are calculated by propagating the statis-tical errors from the simulations through Eqs. (2), (3),and (4). Additionally we have evaluated a 1% system-atic uncertainty on ejection and implantation of H and Be due to the uncertainty in the target thicknesses.
1. Tritium
The model predictions for the ejected and implan-tated activity of tritons in CCD 3 are shown in thethird and fourth columns of Table IV. One can seethat depending on the model, 25%–50% of the tritonsproduced in the CCDs are ejected and there is signif- icant implantation of tritons from the protective alu-minum boxes surrounding the CCDs. Due to the simi-larity of the aluminum and silicon nucleus and the factthat the reaction Q-value for triton production only dif-fers by 5.3 MeV, at high energies the production of tri-tons in aluminum is very similar to that of silicon. InRef. [20], the total triton production cross section as wellas the single and double differential cross sections forneutron-induced triton ejection were found to be thesame for silicon and aluminum, within the uncertaintyof the measurements. This led the authors to suggestthat results for aluminum, which are more completeand precise, can also be used for silicon. We show all ex-isting measurements for neutron- and proton-inducedtriton production in aluminum [46, 47, 84] in Fig. 14along with model predictions. Comparison to Fig. 1shows that all models considered have very similar pre-dictions for aluminum and silicon.This similarity in triton production, as well as thesimilar stopping powers of aluminum and silicon, leadsto a close compensation of the triton ejected from thesilicon CCD with the triton implanted into the CCDfrom the aluminum box. If the material of the box andCCD were identical and there was sufficient materialsurrounding the CCD, the compensation would be ex-act, with no correction to the production required (ig-noring attenuation of the neutron flux). In our case, theratio of production to residual tritons is predicted tobe 0.985 ± Be Due to the heavier nucleus, the fraction of ejected Be nuclei is expected to be smaller than for tritons.As listed in Table V, the Geant4 INCLXX model pre-4
10 Energy [MeV] -
10 110 Cross Section [mbarn] H Al(n,x) H Al(p,x) Konobeyev & Korovin (ACTIVIA)TALYSINCL++ (ABLA 07)Geant4 INCLXXGeant4 BERTINIGeant4 BIC
FIG. 14. Experimental measurements (data points) and modelestimates (continuous lines) of the neutron-induced tritiumproduction in aluminum. Measurements of the proton-induced cross section are also shown for reference. To becompared with Fig. 1. dicts that ∼
17% of Be produced in the silicon wafersis ejected. For the BIC and BERTINI models, the pre-dicted production rates in silicon are roughly 400 timessmaller than our measurement and within the statis-tics of our simulations we could only place upper lim-its on the fraction ejected from the wafers at roughly30%. We chose to use Wafer 3 for our estimation be-cause it has the largest amount of silicon upstream ofthe targets, allowing for the closest compensation of theejection through implantation. However, for Be thereis also a contribution of implantation from productionin the ∼ ( ) mBq for the different models.Because this is significant compared to the severely un-derestimated production and ejection in silicon for theBERTINI and BIC models, the ratio of the production toresidual activity is also greatly underestimated and wehave therefore chosen to not use the BERTINI and BICmodels for estimations of the Be production rate fromhere onwards. For all models without kinematic infor-mation we have used the ratio of production to resid-ual Be activity from the Geant4 INCLXX model, i.e.1.008 ± Na As seen in the third and fourth columns of Table VI,both the ejection and implantation fraction of Na nu-clei are negligible due to the large size of the residualnucleus and no correction needs to be made to the pre-dicted production activity.
B. Comparison to Experimental Measurements
The ratio of the experimentally measured activitiesto the predictions of the residual activity from differ-ent models are shown in the final column of Tables IV,V, and VI for H, Be, and Na respectively. For tri-tium, it can be seen that the predictions of the K&Kand INCL models are in fairly good agreement withthe measurement, while the TALYS model overpredictsand the Geant4 BERTINI and BIC models underpre-dict the activity by more than a factor of two. For Be, the best agreement with the data comes from theS&T model and the spline fit to measurements of theproton-induced cross section. We note that the pro-ton cross sections do slightly overpredict the produc-tion from neutrons, as found in Ref. [45], but the valueis within the measurement uncertainty. For Na, thereis good agreement between our measured activity andthe predictions from the experimental measurements ofthe neutron-induced activity by Michel et al. [58, 59],extrapolated at high energies using the TALYS model.For comparison, the use of the proton-induced produc-tion cross section (shown in Fig. 3) leads to a value thatis roughly 1.9 × larger than our measured activity.If we assume that the energy dependence of the cross-section model is correct, the ratio of the experimentallymeasured activity to the predicted activity is the nor-malization factor that must be applied to each modelto match the experimental data. In the next section wewill use this ratio to estimate the production rates fromcosmic-ray neutrons at sea level. VI. COSMOGENIC NEUTRON ACTIVATION
The isotope production rate per unit target massfrom the interaction of cosmic-ray neutrons, P (cid:48) [atoms/ ( kg sec ) ], can be written as P (cid:48) = n (cid:90) Φ ( E ) · σ ( E ) dE , (6)where n is the number of target atoms per unit massof silicon [atoms/kg], σ ( E ) is the isotope productioncross section [cm ], Φ ( E ) is the cosmic-ray neutronflux [neutrons/ ( cm sec MeV ) ], and the integral is eval-uated from 1 MeV to 10 GeV. While the cross sectionis not known across the entire energy range and eachof the models predicts a different energy dependence,the overall normalization of each model is determinedby the comparison to the measurements on the LAN-SCE neutron beam. The similar shapes of the LANSCE The TALYS cross sections only extend up to 1 GeV [37]. We haveassumed a constant extrapolation of the value at 1 GeV for energies > Model Pred. Cosm. Scaled Cosm. H prod. rate H prod. rate[atoms/ ( kg d ) ] [atoms/ ( kg d ) ]K&K (ACTIVIA) 98 ±
12 108 ± ±
33 96 ± ±
13 114 ± ± ± ± ± ±
14 130 ± H production rates (middle column)from sea-level cosmic-ray neutron interactions in silicon fordifferent cross-section models. The final column provides ourbest estimate of the production rate for each model after scal-ing by the ratio of the measured to predicted H activities forthe LANSCE neutron beam.Model Pred. Cosm. Scaled Cosm. Be prod. rate Be prod. rate[atoms/ ( kg d ) ] [atoms/ ( kg d ) ]S&T (ACTIVIA) 8.1 ± ± ± ± ± ± nat Si(p,x) Be Spl. 9.8 ± ± ± ± Be production rates (middle column)from sea-level cosmic-ray neutron interactions in silicon fordifferent cross-section models. The final column provides ourbest estimate of the production rate for each model after scal-ing by the ratio of the measured to predicted Be activities forthe LANSCE neutron beam. beam and the cosmic-ray neutron spectrum allow us togreatly reduce the systematic uncertainty arising fromthe unknown cross section.There have been several measurements and calcula-tions of the cosmic-ray neutron flux (see, e.g., Refs. [85–87]). The intensity of the neutron flux varies with alti-tude, location in the geomagnetic field, and solar mag-netic activity—though the spectral shape does not varyas significantly—and correction factors must be appliedto calculate the appropriate flux [88]. The most com-monly used reference spectrum for sea-level cosmic-ray neutrons is the so-called “Gordon” spectrum [71](shown in Fig. 7), which is based on measurements atfive different sites in the United States, scaled to sealevel at the location of New York City during the mid-point of solar modulation. We used the parameteri-zation given in Ref. [71], which agrees with the datato within a few percent. The spectrum uncertaintiesat high energies are dominated by uncertainties in thespectrometer detector response function ( <
4% below10 MeV and 10–15% above 150 MeV). We have assignedan average uncertainty of 12.5% across the entire energyrange.The predicted production rates per unit target massfor the cross-section models considered are shown inthe second columns of Tables VII, VIII, and IX for H, Be, and Na respectively. Scaling these valuesby the ratio of the measured to predicted activities forthe LANSCE neutron beam, we obtain our best esti-
Model Pred. Cosm. Scaled Cosm. Na prod. rate Na prod. rate[atoms/ ( kg d ) ] [atoms/ ( kg d ) ]S&T (ACTIVIA) 86 ±
11 43.2 ± ± ± ± ± ± ± ± ± ±
14 43.4 ± ±
15 43.1 ± Na production rates (middle column)from sea-level cosmic-ray neutron interactions in silicon fordifferent cross-section models. The final column provides ourbest estimate of the production rate for each model after scal-ing by the ratio of the measured to predicted Na activitiesfor the LANSCE neutron beam. mates for the neutron-induced cosmogenic productionrates per unit target mass, shown in the correspond-ing final columns. The spread in the values for thedifferent cross-section models is an indication of thesystematic uncertainty in the extrapolation from theLANSCE beam measurement to the cosmic-ray neutronspectrum. If the LANSCE neutron-beam spectral shapewas the same as that of the cosmic-ray neutrons, or ifthe cross-section models all agreed in shape, the cen-tral values in the final column of each table would beidentical.Our best estimate of the activation rate oftritium in silicon from cosmic-ray neutrons is ( ± exp ± cs ± n f ) atoms ( H ) / ( kg day ) , wherethe first uncertainty listed is due to experimentalmeasurement uncertainties (represented by the aver-age uncertainty on the ratio of the measured to pre-dicted activities from the LANSCE beam irradiationfor a specific cross-section model), the second is dueto the uncertainty in the energy dependence of thecross section (calculated as the standard deviation ofthe scaled cosmogenic production rates of the differ-ent models), and the third is due to the uncertaintyin the sea-level cosmic-ray neutron flux. Similarly,the neutron-induced cosmogenic activation rates for Be and Na in silicon are ( ± exp ± cs ± n f ) atoms ( Be ) / ( kg day ) and ( ± exp ± cs ± n f ) atoms ( Na ) / ( kg day ) . VII. ACTIVATION FROM OTHER PARTICLES
In addition to activity induced by fast neutrons, inter-actions of protons, gamma-rays, and muons also con-tribute to the total production rate of H, Be and Na.In the following sub-sections we describe the methodswe used to estimate the individual contributions usingexisting measurements and models. In some cases ex-perimental data is very limited and we have had to relyon rough approximations based on other targets andrelated processes.6
10 Energy [MeV] - - - - - - - - sec MeV)] Particle Flux [1/(cm
Diggory Proton FluxZiegler Proton FluxEXPACS Gamma FluxGordon Neutron Flux
FIG. 15. Comparison of sea-level cosmic-ray fluxes of protons[89–91], gamma rays [93], and neutrons [71].
A. Proton Induced Activity
At sea level the flux of cosmic-ray protons is lowerthan that of cosmic-ray neutrons due to the attenua-tion effects of additional electromagnetic interactions inthe atmosphere. To estimate the production rate fromprotons we have used the proton spectra from Ziegler[89, 90] and Diggory et. al. [91] (scaled by the angulardistribution from the PARMA analytical model [92] asimplemented in the EXPACS software program [93]),shown in Fig. 15.Experimental measurements of the proton-inducedtritium production cross section have been made only ata few energies (see Fig. 1). We have therefore based ourestimates on the neutron cross-section models, scaledby the same factor used in Table IV. To account forpossible differences between the proton- and neutron-induced cross sections, we have included a 30% un-certainty based on the measured differences betweenthe cross sections in aluminum (see Fig. 14). Simi-lar to the neutron-induced production, we have usedthe mean and sample standard deviation of the pro-duction rates calculated with all the different combi-nations of the proton spectra and cross-section modelsas our estimate of the central value and uncertainty,yielding a sea-level production rate from protons of ( ± ) atoms ( H ) / ( kg day ) .For Be and Na, measurements of the protoncross section across the entire energy range have beenmade; we have used spline fits to the data with anoverall uncertainty of roughly 10% based on the ex-perimental uncertainties (see Figs. 2 and 3). Ourbest estimates for the Be and Na production ratesfrom protons are ( ± ) atoms ( Be ) / ( kg day ) and ( ± ) atoms ( Na ) / ( kg day ) .
10 Energy [MeV] - - -
10 1
Cross Section [mbarn] H Si(g,x) nat
TALYS Be Si(g,x) nat
TALYS Na Si(g,x) nat
TALYS H Si(g,x) nat
Scaled TALYS Be Si(g,x) nat
Scaled TALYS Na Si(g,x) nat
Scaled TALYS
FIG. 16. Estimated photonuclear cross-section models for pro-duction of H, Be, and Na. The dashed lines indicate theoriginal models from TALYS while the solid lines indicatethe models scaled to match yield measurements made withbremsstrahlung radiation [94, 95].
B. Gamma Ray Induced Activity
The flux of high-energy gamma rays at the Earth’ssurface was obtained using the PARMA analyticalmodel [92] as implemented in the EXPACS softwareprogram [93]. Similar to the neutron spectrum, we usedNew York city as our reference location for the gammaspectrum, which is shown in Fig. 15.Photonuclear yields of Be and Na in silicon havebeen measured using bremsstrahlung beams with end-points ( E ) up to 1 GeV [94]. We are not aware of anymeasurements of photonuclear tritium production insilicon, though there is a measurement in aluminumwith E =
90 MeV [95] which we assume to be the sameas for silicon. The yields, Y ( E ) , are typically quoted interms of the cross section per equivalent quanta (eq.q),defined as Y ( E ) = (cid:90) E σ ( k ) N ( E , k ) dk E (cid:90) E kN ( E , k ) dk (7)where σ ( k ) is the cross section as a function of pho-ton energy k , and N ( E , k ) is the bremsstrahlungenergy spectrum. To obtain an estimate for σ ( k ) , we assume a 1/ k energy dependence for N ( E , k ) [96] and scale the TALYS photonuclearcross section models to match the measured yieldsof 72 µb/eq.q. at E =
90 MeV for tritium and227 µb/eq.q. and 992 µb/eq.q. at E = Be and Na, respectively (see Fig. 16). This cor-responds to estimated photonuclear production ratesof 0.73 atoms ( H ) / ( kg day ) , 0.12 atoms ( Be ) / ( kg day ) ,and 2.2 atoms ( Na ) / ( kg day ) . Given the large uncer-tainties in the measured yields, the cross-section spec-tral shape, and the bremsstrahlung spectrum, we as-sume a ∼
70% overall uncertainty on these rates.7
Source H production rate Be production rate Na production rate[atoms/ ( kg day ) ] [atoms/ ( kg day ) ] [atoms/ ( kg day ) ]Neutrons 112 ±
24 8.1 ± ± ± ± ± ± ± ± ± ± ± ±
24 9.4 ± ± C. Muon Capture Induced Activity
The production rate of a specific isotope X from sea-level cosmogenic muon capture can be expressed as P µ ( X ) = R · λ c (Si) Q λ d + λ c (Si) · f Si ( X ) (8)where R = ( ± ) µ − / ( kg day ) is the rate ofstopped negative muons at sea level at geomagneticlatitudes of about 40 ◦ [97], the middle term is thefraction of muons that capture on silicon (as opposedto decaying) with the capture rate on silicon λ c (Si) = ( ± ) × / sec [98], the decay rate of muons λ d = 4.552 × / sec [99], and the Huff correction fac-tor Q = f Si ( X ) , is the fraction of muon captures on siliconthat produce isotope X .For Si the fraction of muon captures with chargedparticles emitted has been measured to be ( ± ) %with theoretical estimates [101] predicting the compo-sition to be dominated by protons ( f Si ( H) = 8.8 %), al-phas ( f Si ( He) = 3.4 %), and deuterons ( f Si ( H) = 2.2 %).The total fraction of muon captures that produce tritonshas not been experimentally measured , but a lowerlimit can be set at ( ± ) × − % from an experi-mental measurement of tritons emitted above 24 MeV[102]. Recent measurements of the emission fractionsof protons and deuterons following muon capture onaluminum have found values of f Al ( H) = ( ± ) %and f Al ( H) = ( ± ) % [103], and those same datacan be used to calculate a rough triton emission frac-tion of f Al ( H) = 0.4 % [104]. If one assumes the sametriton kinetic energy distribution in silicon as estimatedfor aluminum [103] and uses it to scale the value mea-sured above 24 MeV, one obtains a triton productionestimate of f Si ( H) = ( ± ) %. The productionrate of tritons from muon capture is then estimated tobe ( ± ) atoms ( H ) / ( kg day ) .The fraction of muon captures that produce Na hasbeen measured at f Si ( Na) = ( ± ) % [105], cor-responding to a production rate from muon captures of A direct measurement of triton production from muon capture insilicon by the AlCap collaboration is expected in the near future. ( ± ) atoms ( Na ) / ( kg day ) . To our knowledgethere have been no measurements of the production of Be through muon capture on silicon. We assume theratio of Be to Na production is the same for muoncapture as it is for the neutron production rates calcu-lated earlier, with roughly 100 % uncertainty, resultingin an estimated production rate from muon captures of ( ± ) atoms ( Be ) / ( kg day ) . VIII. DISCUSSION
The final estimates for the total cosmogenic produc-tion rates of H, Be, and Na at sea level are listed inTable X. These rates can be scaled by the known vari-ations of particle flux with altitude or depth, locationin the geomagnetic field, and solar activity, to obtainthe total expected activity in silicon-based detectors forspecific fabrication, transportation, and storage scenar-ios. The production rate at sea level is dominated byneutron-induced interactions, but for shallow under-ground locations muon capture may be the dominantproduction mechanism. For estimates of the tritiumbackground, implantation of tritons generated in sur-rounding materials and ejection of tritons from thin sil-icon targets should also be taken into account.Tritium is the main cosmogenic background ofconcern for silicon-based dark matter detectors.At low energies, 0–5 keV, the estimated produc-tion rate corresponds to an activity of roughly0.02 decays/ ( keV kg day ) per day of sea-level exposure.This places strong restrictions on the fabrication andtransportation of silicon detectors for next-generationdark matter experiments. In order to mitigate the tri-tium background we are currently exploring the possi-bility of using low-temperature baking to remove im-planted tritium from fabricated silicon devices.Aside from silicon-based dark matter detectors, sili-con is also widely used in sensors and electronics forrare-event searches due to the widespread use of sili-con in the semiconductor industry and the availabilityof high-purity silicon. The relative contributions of H, Be, and Na to the overall background rate of an ex-periment depends not only on the activation rate butalso on the location of these components within the de-tector and the specific energy region of interest. Thecosmogenic production rates determined here can be8used to calculate experiment-specific background con-tributions and shielding requirements for all silicon-based materials.
IX. ACKNOWLEDGEMENTS
We are grateful to John Amsbaugh and Seth Ferrarafor designing the beamline holders, Larry Rodriguezfor assistance during the beam time, and Brian Glasgowand Allan Myers for help with the gamma counting.We would also like to thank Alan Robinson and AndreiGaponenko for useful discussions on production mech-anisms from other particles. This work was performed,in part, at the Los Alamos Neutron Science Center(LANSCE), a NNSA User Facility operated for theU.S. Department of Energy (DOE) by Los Alamos Na-tional Laboratory (Contract 89233218CNA000001) andwe thank John O’Donnell for his assistance with the beam exposure and data acquisition. Pacific NorthwestNational Laboratory (PNNL) is operated by BattelleMemorial Institute for the U.S. Department of Energy(DOE) under Contract No. DE-AC05-76RL01830; theexperimental approach was originally developed un-der the Nuclear-physics, Particle-physics, Astrophysics,and Cosmology (NPAC) Initiative, a Laboratory Di-rected Research and Development (LDRD) effort atPNNL, while the application to CCDs was performedunder the DOE Office of High Energy Physics’ Ad-vanced Technology R&D subprogram. We acknowl-edge the financial support from National Science Foun-dation through Grant No. NSF PHY-1806974 and fromthe Kavli Institute for Cosmological Physics at The Uni-versity of Chicago through an endowment from theKavli Foundation. The CCD development work wassupported in part by the Director, Office of Science, ofthe U.S. Department of Energy under Contract No. DE-AC02-05CH11231. [1] O. Abramoff, et al. (SENSEI), SENSEI: Direct-DetectionConstraints on Sub-GeV Dark Matter from a ShallowUnderground Run Using a Prototype Skipper-CCD,Physical Review Letters 122 (2019) 161801.[2] R. Agnese, et al. (SuperCDMS), First Dark Matter Con-straints from a SuperCDMS Single-Charge Sensitive De-tector, Physical Review Letters 121 (2018) 051301. [erra-tum: Physical Review Letters 122 (2019) 069901].[3] A. Aguilar-Arevalo, et al. (DAMIC), First Direct-Detection Constraints on eV-Scale Hidden-Photon DarkMatter with DAMIC at SNOLAB, Physical Review Let-ters 118 (2017) 141803.[4] R. Essig, M. Fernandez-Serra, J. Mardon, A. Soto,T. Volansky, T.-T. Yu, Direct Detection of sub-GeV DarkMatter with Semiconductor Targets, JHEP 05 (2016) 046.[5] A. Aguilar-Arevalo, et al. (DAMIC), Search for low-mass WIMPs in a 0.6 kg day exposure of the DAMICexperiment at SNOLAB, Physical Review D 94 (2016)082006.[6] R. Agnese, et al. (SuperCDMS), Projected sensitivity ofthe SuperCDMS SNOLAB experiment, Physical ReviewD 95 (2017) 082002.[7] W. von Ammon, H. Herzer, The production and avail-ability of high resistivity silicon for detector application,Nuclear Instruments and Methods in Physics ResearchSection A: Accelerators, Spectrometers, Detectors andAssociated Equipment 226 (1984) 94 – 102.[8] A. Aguilar-Arevalo, et al. (DAMIC), Measurement ofradioactive contamination in the high-resistivity sili-con CCDs of the DAMIC experiment, JINST 10 (2016)P08014.[9] J. Orrell, I. Arnquist, M. Bliss, R. Bunker, Z. Finch, Nat-urally occurring Si and low-background silicon darkmatter detectors, Astroparticle Physics 99 (2018) 9–20.[10] S. Cebrian, Cosmogenic activation of materials, Interna-tional Journal of Modern Physics A 32 (2017) 1743006.[11] R. Agnese, et al. (SuperCDMS), Production Rate Mea-surement of Tritium and Other Cosmogenic Isotopes in Germanium with CDMSlite, Astroparticle Physics 104(2019) 1–12.[12] P. Lisowski, K. Schoenberg, The Los Alamos NeutronScience Center, Nuclear Instruments and Methods A562 (2006) 910–914.[13] B. Takala, The ICE House, Los Alamos Science (2006).[14] C. Dunford, T. Burrows, Online nuclear data service(1998).[15] J. Meija, et al., Isotopic compositions of the elements2013 (IUPAC technical Report), Pure and AppliedChemistry 88 (2016) 293–306.[16] R. Reedy, Cosmogenic-nuclide production rates: Re-action cross section update, Nuclear Instruments andMethods in Physics Research Section B: Beam Interac-tions with Materials and Atoms 294 (2013) 470–474.[17] M. Caffee, K. Nishiizumi, J. Sisterson, J. Ullmann,K. Welten, Cross section measurements at neutron ener-gies 71 and 112 MeV and energy integrated cross sectionmeasurements (0.1 < En <
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