Differentiation of Bulk and Surface Events in p-type Point-Contact Germanium Detectors for Light WIMP Searches
AAS-TEXONO/13-02
Differentiation of Bulk and Surface Events in p-type Point-Contact GermaniumDetectors for Light WIMP Searches
H.B. Li, L. Singh,
1, 2
M.K. Singh,
1, 2
A.K. Soma,
1, 2
C.H. Tseng, S.W. Yang, M. Agartioglu,
1, 3
G. Asryan, Y.C. Chuang, M. Deniz, T.R. Huang, G. Kiran Kumar, J. Li, H.Y. Liao, F.K. Lin, S.T. Lin,
1, 3
S.K. Liu, V. Sharma,
1, 2
Y.T. Shen, V. Singh, H.T. Wong, ∗ Y.C. Wu, Y. Xu,
1, 6
C.X. Yu,
1, 6
Q. Yue, and W. Zhao (TEXONO Collaboration) Institute of Physics, Academia Sinica, Taipei 11529, Taiwan. Department of Physics, Banaras Hindu University, Varanasi 221005, India. Department of Physics, Dokuz Eyl¨ul University, Buca, ˙Izmir 35160, Turkey. Department of Engineering Physics, Tsinghua University, Beijing 100084, China. Department of Physics, Sichuan University, Chengdu 610065, China. Department of Physics, Nankai University, Tianjin 300071, China. (Dated: November 9, 2018)The p-type point-contact germanium detectors are novel techniques offering kg-scale radiationsensors with sub-keV sensitivities. They have been used for light Dark Matter WIMPs searchesand may have potential applications in neutrino physics. There are, however, anomalous surfacebehaviour which needs to be characterized and understood. We describe the methods and results ofa research program whose goals are to identify the bulk and surface events via software pulse shapeanalysis techniques, and to devise calibration schemes to evaluate the selection efficiency factors.Efficiencies-corrected background spectra from the low-background facility at Kuo-Sheng NeutrinoLaboratory are derived.
PACS numbers: 95.35.+d, 29.40.-n,
I. INTRODUCTION
Searches and identification of dark matter [1] are atthe forefronts of experimental research. Germaniumdetectors with sub-keV sensitivities have been demon-strated as efficient means to probe Weakly Interact-ing Massive Particles (WIMPs, denoted by χ ), of massm χ ∼ −
10 GeV [2, 3]. This motivates developmentof p-type point-contact germanium detectors ( p Ge) [4].This novel detector technique is also adopted in the stud-ies of neutrino-nucleus coherent scattering with reactorneutrinos [2]. In both cases, the interaction channel is χ ( ν ) + N → χ ( ν ) + N , (1)where N denotes the nucleus. The experimental signa-tures are the nuclear recoils, posing the challenging re-quirements of low background and low threshold to thedetectors. Allowed region together with annual modu-lation signatures at m χ ∼ σ χN ∼ × − cm were impliedby the CoGeNT experiment [5], while limits were derivedby the TEXONO [6] and CDEX-1 [7] experiments.The surface events in p Ge exhibit anomalous be-haviour [5, 6, 8, 9]. It may limit the physics sensitivi-ties, and can lead to false interpretation of the data. Theanalysis of these anomalous surface events is therefore animportant experimental challenge to overcome before the ∗ Corresponding Author: [email protected] full potentials of this novel detector technique at sub-keVenergy can be realized.We document this aspect of the TEXONO experi-ment [6] in this report. The physics origin, rise-time mea-surements, separation of bulk from surface events as wellas the derivations of efficiency factors and the associateduncertainties are discussed in the subsequent sections.The data adopted to illustrate the analysis proceduresare from a p Ge whose target is a cylindrical germaniumcrystal of 60.1 mm in diameter and 60.8 mm in height.The data size is 39.5 kg-days [6]. The application of thesame analysis on other p Ge detectors or to different dataset from the same detector gives consistent behaviour andresults.
II. EXPERIMENT OVERVIEW
Signals from the point-contact of the p Ge are suppliedto a reset preamplifier. The output is distributed to (a)a fast timing amplifier (TA) digitized at 200 MHz whichkeeps the rise-time information, and (b) a shaping ampli-fier (SA) at 6 µ s shaping time digitized at 60 MHz whichprovides the trigger and measurement of energy (denotedby T ). The pedestal fluctuation RMS is 55 eV ee , thetest pulser FWHM is 141 eV ee while the electronic noiseedge is at 400 eV ee − electron-equivalent energy is usedthroughout in this article to denote detector response.The analysis threshold for this work is 500 eV ee .The detector system is installed at the Kuo-ShengReactor Neutrino Laboratory (KSNL) for the studiesof neutrino physics [10] and light WIMP searches [6]. a r X i v : . [ phy s i c s . i n s - d e t ] M a r FIG. 1: Schematic diagram of the experimental set-up whichincludes the p Ge and NaI(Tl) scintillator. The hardware isplaced inside a 50-ton shielding structure, surrounded by plas-tic scintillators as cosmic-ray vetos.
The schematic diagram of the experimental set-up isgiven in Figure 1. Software pulse shape analysis identi-fies electronic noise background from the physics eventscharacterized by genuine creation of electron-hole pairsin the crystal. The NaI(Tl) crystal scintillator servesas anti-Compton (AC) detector while the surround-ing plastic scintillator panels provide the cosmic-ray(CR) veto. The physics events are categorized by“AC − (+) ⊗ CR − (+) ”, where the superscript − (+) denotesanti-coincidence(coincidence) with the p Ge signals. Theselection procedures as well as the derivation of their ef-ficiencies have been well-established [3, 10] through theseveral experiments conducted at KSNL with this base-line design.The tagging-manifolds correspond to events from dif-ferent physics origins. Nuclear recoil ( χ/ν ) N eventsare uncorrelated with other detector components anduniformly distributed in the p Ge volume. Therefore,the candidate events are tagged by AC − ⊗ CR − , whileAC + ⊗ CR − and AC − ⊗ CR + select ambient gamma andcosmic-ray induced high energy neutron events, respec-tively. In addition, calibration data are taken with lowand high energy γ -sources ( Am at 59.5 keV ee and Cs at 661.7 keV ee , respectively). These sources giverise to events with different penetration-depth distribu-tions, as depicted in Figures 2a&b. They therefore playcomplementary roles in probing the detector responseover the entire active volume. III. BULK AND SURFACE EVENTSA. Physics Origin
The schematic diagram of a typical p Ge sensor is dis-played in Figure 3. The crystal is made of p-type germa- (a)
Event Location (mm)0 10 20 30 40 50 60 A r b i t r a r y U n i t -5 -4 -3 -2 -1 Am Cs Cosmic-ray induced neutrons (b)
Event Location (mm)0.8 1 1.2 1.4 1.6 1.8 2 A r b i t r a r y U n i t -5 -4 -3 -2 -1 Am Cs Cosmic-ray induced neutrons
FIG. 2: (a) The simulated penetration-depth distributionsof various samples: low and high energy γ -rays in Am and
Cs, respectively, as well as cosmic-ray induced high energyneutrons, where energy depositions are less than 6 keV ee afterfolding in the surface quenching effects. The different distri-butions are normalized by their event numbers at the firstbin. (b) Features at surface are elaborated. p + Point Contact n + Surface Electrode [Dead Layer Thickness ∼ r Length ∼ D i a m e t e r ∼ - mm FIG. 3: Schematic diagram of the Ge-crystal in p Ge, showingthe central point-contact and surface electrodes. (a) s) m Time ( N o r m a li ze d P u l s e ( a r b . un i t) B ee
700 eV s) m Time ( N o r m a li ze d P u l s e ( a r b . un i t) S ee
700 eV (b) s) m Time ( N o r m a li ze d P u l s e ( a r b . un i t) B ee s) m Time ( N o r m a li ze d P u l s e ( a r b . un i t) S ee FIG. 4: Typical B/S events at (a) 700 eV ee and (b) 2 keV ee energy, showing the raw (black) and smoothed (blue) pulses,together with the best-fit functions (red). nium. The outer surface electrode is at positive high volt-age towards which the electrons are drifted. The smallcentral contact electrode is at zero-potential from whichelectrical signals are extracted.The outer surface electrode is fabricated by lithiumdiffusion. It has a finite thickness of typically ∼ p Gein this work is measured to be (1.16 ± γ -peaks from a Ba source [11]. In addition, throughthe comparison of the B- and S-intensities and spectrawith the various γ -sources, it can be derived that thereis no charge collection at a depth of less than 0.84 mm.The dead and inactive layers are illustrated in the event (a) ) ee T (keV0 2 4 6 8 10 12 s )] m ( t [ l og -1.5-1-0.500.51 t scan t SurfaceBulkDiscard (b) s)] m ( t [ log -1 -0.5 0 0.5 1 1.5 C o un t ( A r b . U n i t) t Bulk Surface ee Am Cs
137 + CR ˜ - AC - CR ˜ - AC Discard
FIG. 5: (a) The τ versus T scatter plot for the AC − ⊗ CR − tags which select ( χ/ν ) N candidate events. (b) The τ distri-bution at 700 eV ee , comparing the candidate events with thoseof Am,
Cs, and cosmic-induced neutrons (AC − ⊗ CR + ).The various histograms are normalized by the areas of thebulk band. location distributions of Figures 2a&b. Only events withcomplete charge collection are considered as bulk events.The corresponding fiducial mass for the B-region is 840 g.This anomalous surface charge collection effect hasbeen studied in early literature [8]. However, thequenched S-signals are mostly (cid:46) ee , below the typi-cal Ge detector threshold of a few keV ee . Consequently,the S-layer in p-type germanium detectors were mostlyclassified as “dead”. With the advent of p Ge and thephysics region of interest moving to the sub-keV range,it was observed [5, 6, 9] that these anomalous S-eventsdo exist and would dominate the low energy background.The identification of the S-events and the knowledge ofefficiency factors therefore become crucial to fully exploit
Bulk-Band Surface-BandLE ME HE | LE ME HE < τ > ( µ s) 0.52 0.31 0.35 | σ fit ( µ s) 0.025 0.023 0.009 | σ i ( µ s) 0.065 | σ m ( µ s) 1.21 0.28 0.11 | σ τ ( µ s) 1.21 0.27 0.09 | | < τ > − τ | / σ m | τ ) measurements for bulk (B) and surface (S) bands at low (LE: 500 −
700 eV ee ),medium (ME: 1.5 − ee ) and high (HE: 6 − ee ) energy. All width and resolution values correspond to the RMS of thedistributions with the mean-values at < τ > . The fitting errors ( σ fit ) correspond to those due to the analysis algorithms.The intrinsic width ( σ i ) is defined by the surface-dominating Am events at 10 keV ee and by the homogeneously-distributedGa-X-rays at 10.37 keV ee for the S- and B-bands, respectively. Combining σ i and the τ -resolution ( σ τ ) in quadrature gives themeasured width of the band ( σ m ). The optimal τ -cut ( τ ) is set at 1.23 µ s. The last row characterizes the separation of < τ > from τ , in unit of σ m . the sub-keV sensitivities of p Ge.
B. Rise-time Measurement
Typical TA-signals for B/S-events at low ( ∼
700 eV ee )and high ( ∼ ee ) energy are depicted in Figures 4a&b,respectively. The TA rise-time ( τ ) is parametrized by thehyperbolic tangent function12 A × tanh( t − t τ ) + P , (2)where A , P and t are, respectively, the amplitude,pedestal offset and timing offset. The values of P andA are evaluated from the TA-pulses prior to the tran-sition edge and through the difference of the asymptoticlevels, respectively. The time difference as a function ofenergy between the TA-edge and the DAQ-trigger instantdefined by the SA signals is pre-determined, and providesconstraints on t . The raw TA-pulses are first smoothedby the Softies-Kola filter [12] and fitted to Eq. 2 with( τ ,t ) as free parameters. The results are then adopted asinitial values to another fit of the same function directlyon the raw pulse. The two procedures are complemen-tary − t and τ are sensitive to the smoothed and rawpulses, respectively. The smoothed and best-fit functionsare overlaid to the raw FADC signals in Figure 4.A small fraction ( < + ⊗ CR + samples, which is 80% at 500 eV ee .The scatter plot of τ versus T for the AC − ⊗ CR − events at KSNL is displayed in Figure 5a. Events with τ less(greater) than a selected cut-value τ (=1.23 µ s inthis analysis) are categorized as B(S). A summary of thewidth and resolution contributions to the bands is givenin Table I. The fitting errors ( σ fit ) correspond to thosedue to the software algorithms. They are small comparedto the measured width ( σ m ) from the various calibration data set. There are two contributions to the τ -width:(i) the intrinsic width σ i is due to the non-uniform re-sponse over the detector volume producing different τ ,while (ii) the τ -resolution σ τ is due to fluctuations ofpulse shape for events at the same nominal τ . The σ i ’sare measured from the surface-dominating Am eventsat 10 keV ee and the homogeneously-distributed Ga-X-rays at 10.37 keV ee for the S- and B-bands, respectively,while σ τ is derived via σ τ = σ m − σ i .At T > . ee , the σ m is much less than the sep-aration of the bands from τ . The measurements of τ therefore provide valid information on the locations ofthe events and, in particular, can efficiently differenti-ate the S- from B-events. This behaviour manifest as adistinct two-band structure in Figure 5a, with a smallfraction (about 8% within 3 − ee in the AC − ⊗ CR − sample) of events in the intermediate transition zone.By studying the corresponding fractions of events with Am ( < Cs (7.5%) γ -sources, a thicknessof 0.16 mm for this zone is derived. The choice of τ is equivalent to a definition of the spatial borderline be-tween B/S within this transition thickness. This givesrise to a systematic uncertainty in the evaluation of the p Ge fiducial mass. It translates to about 3% of the to-tal error at 500 eV ee which, as displayed in Table II, isnegligible compared to the other error sources.At T < . ee where σ m is comparable to the bandseparation, there exist contaminations between the B-and S-events which lead to the merging of the bands.The methods and results to evaluate the leakage factorsand to correct the measured spectra are discussed in thesubsequent sections.The τ -distribution of the candidate samples at700 eV ee are displayed in Figure 5b, together with thosedue to low and high energy γ -rays and high energy neu-trons. The B-events near analysis threshold have simi-lar distributions for all samples and are independent oflocations. Different distributions in the S-events are ob-served. These can be accounted for by their differentpenetration profiles depicted in Figure 2b. (a)(b) FIG. 6: Averaged shapes of the (a) fast timing and (b)shaped pulses of events due to random trigger, test pulserand physics-samples with the AC + ⊗ CR + tag. Anomalously slow rise-time events are observed in ex-cess at low energy from the AC − ⊗ CR − samples. Theirorigin is not yet identified − electronic noise is a possibil-ity since such events are uncorrelated with other detec-tor components. These large- τ events are categorized as“Discard” in Figure 5, and are rejected in the subsequentanalysis. The σ τ of the B-band at 500 eV ee is 1.2 µ s, suchthat the mean is about 4.5 RMS from the Discard region.The leakage of B-events is negligible, and there is no lossin signal efficiencies. IV. EFFICIENCIES MEASUREMENT ANDCORRECTIONA. Formulation
Calibration of the BS-cut requires the measurement ofthe bulk-signal retaining ( (cid:15) BS ) and surface-background (a) ) ee T(keV0.5 1 1.5 2 2.5 3 A r b . U n i t TotalB (MC) B Am Source = g (b) ) ee T(keV A r b . U n i t TotalB (MC) B Cs Source = g (c) ) ee T(keV A r b . U n i t + CR ˜ - Ge AC p B ˜ + CR ˜ - Ge AC p + CR ˜ - Ge) AC n ( B Cosmic-Ray (n)
FIG. 7: The derivation of ( (cid:15) BS , λ BS ) − The measured Totaland B spectra from p Ge with the surface-rich γ -ray − (a) Am, (b)
Cs, as well as (c) the bulk-rich cosmic-ray in-duced neutrons. They are compared to reference B-spectraacquired through simulations for γ -rays and n Ge measure-ment for cosmic-neutrons. suppressing ( λ BS ) efficiencies. This is achieved by relat-ing these efficiency factors with the observed and actualrates, denoted by (B,S) and (0¯,S ), respectively.The normalization assignment (0¯,S )=(B,S) is madeon events within T =2.7-3.7 keV ee . It is equivalent tosetting (cid:15) BS and λ BS to 1.0. This energy range is selectedsince it is above the complications of the L-shell X-rays (a) ee + CR ˜ - n : AC Cs Am BS l BS ˛ BS ˛ (b) ee + CR ˜ - n : AC Cs Am l BS ˛ FIG. 8: Allowed bands of ( (cid:15) BS , λ BS ) derived by solving thecoupled equations in Eq. 3 on the calibration data set, at (a)0.5 − ee , and (b) an energy bin at 2.2 keV ee . at ∼ ee as well as the physics region in dark matteranalysis.At lower energy, (B,S) and (0¯,S ) are related by thecoupled equations:B = (cid:15) BS ·
0¯ + (1 − λ BS ) · S S = (1 − (cid:15) BS ) ·
0¯ + λ BS · S , (3)with an additional unitarity constrain: 0¯+S =B+S. Thederivation of ( (cid:15) BS , λ BS ) therefore involves at least twomeasurements of (B,S) where the actual rates (0¯,S ) areknown. B. Calibration Data
The averaged TA and SA pulse shapes of AC + ⊗ CR + physics samples, together with random trigger and testpulser events, are displayed in Figures 6a&b, respectively.The pulser events exhibit different profiles as thephysics samples, and therefore are not appropriate for (a) ) ee T(keV0.5 1 1.5 2 2.50.60.70.80.91 ˛ BS ˛ BS ˛ (Ga X-ray) (b) ) ee T(keV BS ll FIG. 9: The measured (a) (cid:15) BS and (b) λ BS as functions ofenergy. Independent measurement on (cid:15) BS with Ga-L X-raysis included. calibration purposes. (We note, however, that the lead-ing edge of their shaped pulses are identical, such thatpulser events can be applied in the measurement of trig-ger efficiencies.) Calibration data with Am,
Cs and in situ cosmic-ray induced fast neutrons are adopted in-stead. They have vastly different distributions in theirevents locations within the detector as illustrated in Fig-ure 2a, and hence can play complementary roles in thecalibration.1.
Surface-rich events with
Am and Cs γ -ray sources − As displayed in Figures 7a&b, the measured B-spectra are compared to the reference B derivedfrom full simulation with surface layer thickness of1.16 mm as input. The simulated B-spectra due toexternal γ -sources over a large range of energy areflat for T <
10 keV ee .Consistent results are obtained for different sourceorientations relative to the p Ge sensor. Theadopted data for analysis are those with sourcesplaced at the top facing the flat surface of the p Gecrystal. They provide the most accurate measure-ments since this is the direction where the passivematerials between the sources and the crystal areminimal and their thickness is the most uniform byconstruction.2.
Bulk-rich events with cosmic-ray inducedfast neutrons − A 523 g n-type point-contact germanium ( n Ge) de-tector was constructed. The components and di-mensions are identical to those of p Ge. The surfaceof n Ge is a p + boron implanted electrode of sub-micron thickness. There are no anomalous surfaceeffects. Data are taken under identical shieldingconfigurations at KSNL. The trigger efficiency is100% above T=500 eV ee , and energy calibration isobtained from the standard internal X-ray lines.The AC − ⊗ CR + condition selects cosmic-ray in-duced fast neutron events without associated γ -activities, which manifest mostly as bulkevents. This tag in n Ge is therefore takenas the B-reference and compared with those ofAC − ⊗ CR + ⊗ B in p Ge, as depicted in Figure 7c.
C. Results on ( (cid:15) BS , λ BS ) Using the calibration data discussed above, ( (cid:15) BS , λ BS )are derived by solving the coupled equations in Eq. 3.The three allowed bands at 0.5 − ee and at2.20 − ee are illustrated in Figures 8a&b, respec-tively. The different orientations of the bands are con-sequences of different B:S ratios which are due to thedifferent penetration-depth distributions of Figure 2a.The surface-rich γ -events and the bulk-rich cosmic-rayinduced neutron-events play complementary roles in con-straining λ BS and (cid:15) BS , respectively. The bands have com-mon overlap regions, indicating the results are valid forthe entire detector volume. It is therefore justified toapply ( (cid:15) BS , λ BS ) derived from the calibration data to thephysics samples.The energy dependence of ( (cid:15) BS , λ BS ) are displayed inFigures 9a&b. By comparing the measured in situ Ga-LX-ray peak at 1.3 keV ee after BS-selection to that pre-dicted by the corresponding K-peak at 10.37 keV ee , anadditional data point on (cid:15) BS is independently measured.This provides a cross-check to the calibration proceduresand indicates consistent results.The measured ( (cid:15) BS , λ BS ) are close to unity at T > . ee . It follows from σ m being less than the separa-tion of the bands from τ . There is no leakage betweenthe B- and S-events originated away from the transitionzone. The ambiguity in the B/S assignment to eventswithin the zone is accounted for through a systematicuncertainty on the fiducial mass, which is negligible com-pared to the total error from Table II. (a) ) ee T(keV - CR ˜ - AC B ˜ - CR ˜ - AC ) ee - k e V - d ay - R a t e ( k g B ˜ - CR ˜ - AC ) ee T(keV0 2 4 6 8 10 12 14 16 S ˜ - CR ˜ - AC ) ee - k e V - d ay - R a t e ( k g (b) ) ee T ( keV0.5 1 1.5 2 2.5 3 ) - ee k e V - d ay - R a t e ( k g B ˜ - CR ˜ - AC FIG. 10: (a) Measured and corrected spectra of theAC − ⊗ CR − tag. (b) Shown in magenta are flat backgrounddue to high-energy γ -rays from ambient radioactivity, andcontributions from the L-shell X-rays. Depicted in inset isthe residual spectrum after background subtraction, corre-sponding to candidate ( χ/ν ) N events. V. EFFICIENCIES-CORRECTEDBACKGROUND SPECTRAA. Efficiencies-Corrected Spectra
Once ( (cid:15) BS , λ BS ) are measured with the calibrationdata, the efficiency-corrected (0¯,S ) of the physics sam-ples can be derived via the solution of Eq. 3:0¯ = λ BS · B − (1 − λ BS ) · S( (cid:15) BS + λ BS − = (cid:15) BS · S − (1 − (cid:15) BS ) · B( (cid:15) BS + λ BS − . (4)The formulae can be understood as follows: 0¯(S ) shouldaccount for the loss of efficiency in the measurement ofB(S) in the first positive term, followed by a subtractionof the leakage effect from S(B) in the second negative Energy Bin 0.50 − ee − ee − ee Measurement and Total Error (kg − keV − day − ) 10.6 ± ± ± † :I) Uncertainties on Calibration ( (cid:15) BS , λ BS ) from Fig. 9 : 0.26 0.064 < { { { / ( (cid:15) BS + λ BS −
1) 2.29 1.07 1.00Combined 0.95 0.96 0.99III) Systematic Uncertainties due to Parameter Choice :(i) Rise-time Cut-Value τ { { { τ )=(B,S) at Normalization 0.08 0.03 0.03(v) Choice of Discard Region 0.05 0.01 0.001Combined Systematic Error 0.20 0.27 0.12TABLE II: Contributions to the uncertainties on the AC − ⊗ CR − ⊗
0¯ spectrum from various sources. † Errors are combined inquadrature. The total error is normalized to 1.0. term.The AC − ⊗ CR − tagged events from p Ge data takenat KSNL at various stages of the analysis are depictedin Figure 10a. The measured-B and corrected-0¯ spectraare almost identical. At
T > . ee , this is a di-rect consequence of (cid:15) BS = λ BS = 1. At low energy, theefficiency-correcting and background-subtracting effectscompensate each other in this data set.After subtracting a flat background due to high en-ergy γ -rays and the known L-shell X-rays contributionspredicted by the accurately-measured K-peaks at higherenergy, the residual spectrum is shown in the inset ofFigure 10b. It still shows excess of events at the sub-keVregion. The origin is not yet identified, and the studies to-wards the understanding of which are intensely pursued.Under the conservative assumption that WIMPs signalscannot be larger than the residual excess, constraints on χN cross-section versus m χ were derived. They probedand excluded some of the allowed regions on light WIMPsfrom earlier experiments [6]. B. Error Sources and Assignment
The errors on ( (cid:15) BS , λ BS ) are shown in Figures 9a&b.They are derived from the global fits on the allowed bandsin Figure 8. Standard error propagation techniques areapplied to derive the resulting uncertainties on (0¯,S ) viaEq. 4.The uncertainties include contributions from their ownmeasurement errors, the ( (cid:15) BS , λ BS ) calibration errors, aswell as systematic uncertainties. Their relative contribu-tions in three representative energy bins are summarizedin Table II. The leading contribution is the statistical er-rors on (B,S), scaled by a factor 1/( (cid:15) BS + λ BS − (cid:15) BS and λ BS deviatefrom unity towards the analysis threshold of 500 eV ee . Systematic uncertainties on the BS-selection proce-dure originate from the choice of τ and its effect on the p Ge fiducial mass, the choice of the normalization energyrange at T , the assignment of (0¯,S )=(B,S) in this inter-val, as well as the choice of the Discard region. They areestimated by the shifts in 0¯ as the parameters are variedin the vicinity of their optimal values. As an illustratedexample, the “ τ -scan” range for τ is depicted in Fig-ure 5a. In all cases, the shifts are small compared to thetotal errors. Accordingly, the contributions of systematicuncertainties are minor, as illustrated in Table II. VI. CONCLUSION AND PROSPECTS
The results on ( (cid:15) BS , λ BS ) calibration and the subse-quent (0¯,S ) measurements in p Ge confirm that bothsignal efficiencies and background leakage to the signalregion are crucial in the analysis, all the more so sincethe efficiency factors are significantly less than unity atthe analysis threshold, which is 500 eV ee in this work. Amis-placement of λ BS =1 would introduce excess of eventsat low energy which could have been mis-interpreted assignatures of light WIMPs. Conversely, genuine WIMPsignals can also be masked out through an incorrect as-signment of the factors.We note that it is necessary to derive ( (cid:15) BS , λ BS ) and(0¯,S ) by solving the coupled equations Eq. 3 to obtainEq. 4. If the two efficiency corrections were performedseparately, an incorrect expression of 0¯ = B /(cid:15) BS − [(1 − λ BS ) · S /λ BS ] would follow. Deviations from the correctvalues would depend on the B:S ratio, and would be morepronounced when ( (cid:15) BS , λ BS ) decrease. A relative error oforder unity would be introduced to 0¯ for this data set atthreshold. We note that this comment as well as Eqs. 3&4also apply to generic event selection procedures in cut-based analysis.Despite advances in the BS-selection and efficiency fac-tors measurements discussed in this report, there arestill fundamental challenges to further boost the sensi-tivities on the studies of sub-keV events with p Ge. The1/( (cid:15) BS + λ BS −
1) factor of Eq. 4 increases the uncertain-ties to the physics signal 0¯ near threshold. In addition, 0¯depends on measurements of all of the input parameters( (cid:15) BS , λ BS ,B,S). This calls for caution in the investigationsof time variation and modulation effects on 0¯, in whichthe time stabilities of these input have to be indepen-dently monitored.To overcome these difficulties, the elimination of theanomalous surface effects at the hardware raw signal levelin Ge detectors is much more desirable. To these ends,the merits and operation of n Ge are being studied. Thisdetector has already proved crucial to provide calibrationdata to the p Ge. Research efforts are being pursued to turn it into a target with comparable sensitivities.A by-product of this investigation is that the p Ge τ dis-tributions are different for different sources, as depictedin Figure 5b. Therefore, the studies of signal rise-timemay shed light on the nature of the background. Furthersystematic and quantitative studies are under way. VII. ACKNOWLEDGMENT
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