research article the potential of hybrid pixel detectors...

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2013 Article ID 105318 20 pageshttpdxdoiorg1011552013105318

Research ArticleThe Potential of Hybrid Pixel Detectors in the Search forthe Neutrinoless Double-Beta Decay of 116Cd

Thilo Michel1 Thomas Gleixner1 Juumlrgen Durst2

Mykhaylo Filipenko1 and Stefan Geiszligelsoumlder1

1 Erlangen Centre for Astroparticle Physics (ECAP) Friedrich-Alexander-Universitat Erlangen-Nurnberg Erwin-Rommel-Str 191058 Erlangen Germany

2 Faculty of Physics Ludwig-Maximilians-Universitat Munchen Schellingstr 4 80799 Munchen Germany

Correspondence should be addressed toThilo Michel thilomichelphysikuni-erlangende

Received 28 June 2013 Revised 17 September 2013 Accepted 19 September 2013

Academic Editor Vincenzo Flaminio

Copyright copy 2013 Thilo Michel et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We investigated the potential of the energy resolving hybrid pixel detector Timepix contacted to a CdTe sensor layer for the searchfor the neutrinoless double-beta decay of 116Cd We found that a CdTe sensor layer with 3mm thickness and 165 120583m pixel pitchis optimal with respect to the effective Majorana neutrino mass (119898

120573120573) sensitivity In simulations we were able to demonstrate a

possible reduction of the background level caused by single electrons by approximately 75 at a specific background rate of 10minus3counts(kg times keV times yr) at a detection efficiency reduction of about 23 with track analysis employing random decision forestsExploitation of the imaging properties with track analysis leads to an improvement in sensitivity to 119898

120573120573by about 22 After 5

years of measuring time the sensitivity to 119898120573120573

of a 420 kg CdTe experiment (90 116Cd enrichment) would be 59meV on a 90confidence level for a specific single-electron background rate of 10minus3 counts(kg times keV times yr) The 120572-particle background canbe suppressed by at least about six orders of magnitude The benefit of the hybrid pixel detector technology might be increasedsignificantly if drift-time difference measurements would allow reconstruction of tracks in three dimensions

1 Introduction

The question of whether or not neutrinos are their ownantiparticles still has not been answered In many experi-ments researchers have to cope with large backgrounds to beable to see if neutrinoless double-beta decay (0]120573120573) occursin nature or not An observation of one single neutrino-less double-beta decay would directly prove the Majoranacharacter of neutrinos via the Schechter-Valle theorem [1]Besides this a measurement of the decay rate Γ (or the half-life 1198790]12

= Γminus1) of neutrinoless double-beta decay allows the

determination of the effectiveMajorana neutrinomass whichis given by

119898120573120573

=119898119890

radic1198790]12

times 1198660] (119876120573120573 119885) times

10038161003816100381610038161198720]10038161003816100381610038162

=

1003816100381610038161003816100381610038161003816100381610038161003816

3

sum

119894=1

1198802

119890119894times 119898119894

1003816100381610038161003816100381610038161003816100381610038161003816

(1)

where 119898119890is the electron rest mass 119866

0](119876120573120573 119885) is thecalculable factor for the decay specific phase-space volume

|1198720]|2 is also the calculable nuclear matrix element and the

119880119890119894are elements of the mixing matrix which describes

neutrinomixing of the three mass eigenstates with masses119898119894

to the electron neutrino 119885 is the nuclear charge and 119876120573120573

isthe 119876-value of the double-beta decay Thus a measurementof the half-life of 0]120573120573-decay gives information on themassesof the mass eigenstates and the elements of the mixingmatrix which depends on the mixing angles 120579

12 12057923 12057913

and potentially on CP-violating phases [2] If neutrinos areMajorana fermions two Majorana phases 120572

1and 120572

2appear

in the mixing matrix in addition to the Dirac phase 120575 Inthe Majorana case the mixing matrix reads = PMNS times

diag (1 1205721 1205722) where PMNS is the Standard Model PMNS-

matrix describing Dirac neutrinos and diag (1 1205721 1205722) is a

3 times 3 diagonal matrix with the entries 1 1205721 1205722on the main

diagonalOn a microscopic scale the signatures of double-beta

decays (neutrino accompanied and neutrinoless) are different

2 Advances in High Energy Physics

from most other reactions that might also release energyin the region of the 119876-value of the double-beta decay twoelectrons start simultaneously at one location and travelthrough the detector materials In contrast to neutrinoaccompanied double-beta decay (2]120573120573) the summed kineticenergies of the two electrons from 0]120573120573-decay equal the totalenergy released in the decay (119876-value) Energy resolutionbackground reduction and mass increase are the keys forimproving sensitivity to the effective Majorana neutrinomass If a detector could be built that is able to ldquoimagerdquo thetwo electrons starting at one location most background par-ticles would be eliminated 120572-particles Compton scatteredelectrons electrons and positrons from beta decays (120573minus 120573+)and muons Beta decays to excited states with subsequentinternal conversion of 120574-line photons could still have a similartrack topology but could be identified because the internalconversion electron has a defined energy

The experiments SuperNEMO [3] and the NeutrinoXenon TPC (NEXT) [4 5] plan to perform tracking withor in gaseous detectors Semiconductor detector materialsmdashwhich can in principle serve as sensor materials in hybridpixel detectorsmdashare used in the experiments GERDA [6]Majorana [7] and COBRA [8] The tracking option withCdTe semiconductor pixel detectors has been evaluated asan additional possible route in the COBRA collaboration[8] The ldquoCurrent status and perspectives of the COBRAexperimentrdquo are described in detail also in this special issueof Advances in High Energy Physics by Fritts et al [9]Background studies with silicon sensor pixel detectors havealready been presented in [10] Hybrid pixel detectors are alsoan interesting option for the still missing direct detection ofneutrino accompanied double electron capture [11]

Hybrid pixel detectors comprise pixelated semiconductorsensor layers for particle detection We are thus restrictedto double-beta decay nuclides of elements which cancompose semiconducting materials The technology ofhybrid pixel detectors with silicon sensors is matureThe development of hybrid pixel detectors connected toGermanium sensors is still ongoing CdTe and Cd(Zn)Te finepitch hybrid pixel detectors have already been developedmainly for X-ray imaging for energies from 3 keV to150 keV The elements cadmium tellurium and zincoffer several isotopes that decay via 120573

minus120573minus 120573+120573+ 120573+EC

ECEC 70Zn 114Cd 116Cd 128Te 130Te 106Cd 64Zn 120Te108Cd 116Cd decays via the neutrino accompanied 120573

minus120573minus-

decay to the ground state of 116Sn with the largestQ-value of 2814MeV in the Cd Te Zn complexThe phase-space factor for the 0]120573120573-decay of 116Cd is1198660](119876120573120573 119885) = 468 times 10

minus14 yrminus1 [12] The matrix element|1198720]| is about 35 [13] but the values given in the literature

vary strongly depending on the calculation model The half-life of the 2]120573120573-decaywasmeasured by Bongrand et al [14] tobe1198792]12

= [288plusmn004 (stat)plusmn016 (syst)]times1019 yr Danevich

et al [15] have set a limit of 1198790]12

= 17 times 1023 yr to the

half-life of the 0]120573120573-decay channelThe COBRA-experiment(Cadmium Zinc Telluride 0-neutrino double-beta ResearchApparatus) proposed by Zuber [8] is located in the GranSasso National Laboratory (LNGS) COBRA focuses on

the possible detection of the 0]120573120573-decay in 116Cd withsemiconducting CdZnTe detectors whereby the cadmiumwill be enriched in the isotope 116Cd The original proposalof Zuber [8] is focused on the use of many monolithic cubicCdZnTe detectors with medium size of a few cm3 Theyare larger in volume than the typical sensor layer of a pixeldetector but smaller than the germanium diodes employedin the GERDA experiment [6] Each CdZnTe crystalsshould be read out individually This option is the mainroute of the COBRA collaboration because experimentalcomplexity and technical challenges are less demandingthan in the case of a large-scale experiment with 420 kgof CdTe pixel detectors Such a large mass is necessaryto access the inverted hierarchy neutrino mass schemewhere 119898

3lt 1198981

lt 1198982 in reasonable measuring time One

additional direction that has been followed in the COBRAstudy was the exploitation of CMOS-based hybrid activepixel detectors with a sensor layer of the II-VI-semiconductorCdTe The idea is that the topological structure of the tracksof the two decay electrons from a 0]120573120573-decay of 116Cdmightbe used to discriminate between 0]120573120573-events and singleelectrons from background processes Possible backgroundprocesses include electrons from beta decays of radioactiveimpurities Compton scattering of high-energetic photonscaused by thermal neutron capture in any remaining 114Cdimpurities or photon production after decays of radioactiveimpurities in the detectors

Hybrid pixel detectors comprise an Application SpecificIntegrated Circuit (ASIC) realized in CMOS technology anda semiconductor sensor layer coupled pixel-wise to the ASICby bump-bonding techniques The ASIC is electronicallysegmented in both a matrix of pixels and a periphery forcontrolling and read-out of the pixel matrix Hybrid pixeldetectors have their origins in high-energy physics and area very important part of the tracking systems in the LHCexperiments In ATLAS CMS and ALICE tracking of high-energy charged particles is performed close to the vertexby detecting the energy depositions of charged particles inseveral layers of pixel detectors with silicon sensor layersIn LHCb hybrid pixel detectors with silicon sensors areused to detect accelerated photoelectrons released fromphotocathodes by Cherenkov photons in the RICH detectorsThe Timepix3 detector [16] which has just been developedby the Medipix collaboration might be a promising optionfor a LHCb particle telescope to replace the current sili-con microstrip system in the SLHC era Can hybrid pixeldetectors also help in neutrino physics experiments to decidewhether the neutrino has Dirac or a Majorana characterBy how much can one reduce the background with trackanalysis

2 Materials and Methods

21 The Timepix Detector The base of this study is the state-of-the-art hybrid active pixel detector Timepix [17] which iscompatible with CdTe sensor layers The Timepix detectorhas been developed by the Medipix collaboration [18] in theframework of the EUDET study It is manufactured with the025 120583mCMOS technology and features a 256 times 256 square

Advances in High Energy Physics 3

matrix of electronic cells with 55 120583m pixel pitch The area ofthe active matrix is 14 times 14 cm2 Each of the electronicscells has a metallic input pad that can be connected by meansof bump bonding to the electron collecting electrode of aCdTe layer

It has already been demonstrated that 1mm thick CdTelayers can be assembled with the Timepix ASIC [19 20]Other hybrid pixel detectors like the HEXITEC detectoralready have been successfully contacted to even 3mm thickCdZnTe sensors with 80 times 80 pixels at 250120583m pixel pitch[21] By extending the pixel electrodes of the CdTe layerlaterally over several Timepix electronic pixel cells one canrealize sensor pixel sizes of a multiple of the active matrixpixel pitch (55 120583m) The average energy loss of an ionizingparticle traveling through the sensor that is necessary tocreate an electron-hole pair is 443 eV in CdTe Positive andnegative charge carriers are separated from each other by anelectric field generated through a voltage difference betweenthe common electrode and the pixel electrodes The polarityof the voltage is chosen in a way that the electrons having alarger mobility of 120583

119890asymp 1100 cm2 Vminus1 sminus1) and mobility-life-

time product (120583120591)119890asymp 30 times 10

minus3 cm2 Vminus1 than holes (120583ℎasymp

100 cm2 Vminus1 sminus1 (120583120591)ℎ

asymp 20 times 10minus4 cm2 V minus1) [22] drift

towards the pixel electrodes Both charge carrier types inducemirror charges on the pixel electrode plane The inducedcurrent caused by changes in themirror charge in time due tothe driftmotions is transferred to the input of the electronicspixel cell by the bump bond In the Timepix electronicspixel cell this current pulse is amplified and converted to avoltage pulsewith a peaking time of approximately 100 ns [23](depending on the adjustable preamplifier gain) and a ratherlong falling edge with a duration in the microsecond rangeThe shaped pulse is input to a leading-edge discriminator thatgenerates a gate to a counter The minimum discriminatorthreshold that can be applied in conjunction with a siliconsensor with 55 120583m pixel pitch is about 900 electrons In thecase of a 1mm thick CdTe sensor with 110 120583m pixel pitch wewere able to achieve a minimum threshold of 1185 electronswhich corresponds to 55 keV

Thegate is open as long as the output pulse of the amplifieris above threshold (time-over-threshold mode) or extendsuntil a global shutter signal inhibits the counter (time-of-arrivalmode or time-of-detectionmode)The counter countsthe number of cycles of a clock signal supplied from thematrix periphery to each pixel as long as the gate is openThe maximum clock frequency that can be used in theTimepix is approximately 120MHz In time-over-thresholdmode the counter value represents the length of the amplifieroutput pulse being above threshold This duration is relatedto the induced current integrated over the shaping timewhich corresponds to the amount of charge collected bythe pixel Thus the time-over-threshold is a measure of theenergy deposited by the ionizing particle in the sensitivevolume of the pixel In time-of-detection mode the numberof clock cycles measured in the counter of a pixel representsthe moment of detection with respect to the moment ofappearance of the shutter signal which stops all countingactivity The moment of detection differs from the arrival

time of the particle in the pixel One reason is that a certaindrift length has to be traversed until the influenced currentintegrated over the shaping time of the preamplifier exceedsthe threshold level The maximum drift time of chargecarriers to the pixel electrodes is 735 ns for a 3mm thickCdTe sensor biased at minus1500V Additionally the time walk inthe leading edge discriminator causes a delay of up to 100 nsdepending on energy deposition and threshold level Eachpixel can also be operated in counting mode The counterthen counts the number of particles with energy depositionsabove threshold in the pixel during the shutter opening time

Each pixel can be operated in exactly one of these threemodes and thus deliver images of the number of detectedevents images of energy depositions or images of timestamps The Timepix can in principle deliver all necessaryinformation for 0]120573120573-decay detection the topology of theparticle track the energy deposition in each pixel andthe timing of the event The next version of the Timepixdetectormdashthe Timepix3 [16]mdashwill provide energy informa-tion and timing information simultaneously in each pixel

22 The Detector Simulation221 Signal Generation A Monte-Carlo simulation wasdeveloped for the precise simulation of electron tracks emerg-ing from 0]120573120573-decays and for single electrons emergingfrom beta decays or Compton scatteringThe event generatorDecay0 [24] was used to generate the momenta of the twoelectrons emerging from 0]120573120573-decays distributed homoge-neously in the CdTe layer In the Monte-Carlo simulationframework ROSI [25] which is based on EGS4 with the low-energy extension LSCAT the tracks were sampled with stepsof a few micrometers Each track consisted of segments Anew segment was forced after an energy loss of 1 of theactual electron energy at most We modeled the signal gen-eration in the CdTe pixel detector as follows The energy lossΔ119864119894along a segment 119894 was converted to the corresponding

number of generated electron-hole pairs 119873119894= Δ119864119894(443 eV)

to calculate the contribution of the charge carriers released insegment 119894 to the induced current at the pixel electrode planeThe drift time was calculated for each segment 119894 taking theaverage distance of the track segment to the pixel electrodeplane and the electric field strength into accountThe electricfield strength as a function of the distance from the pixelelectrode 119911 was calculated for every combination of sensorthickness and bias voltage 119880 by || = |119880| sdot (119891

1sdot 119911 + 119891

2+

1198913sdot 119890minus|119880|sdot119891

4sdot119911] We obtained 119891

1= (580 plusmn 009) times 10

5mminus21198912= (2280plusmn75)mminus1 119891

3= (540plusmn144)mminus1 and 119891

4= (479plusmn

216) Vminus1mminus1 by fitting electric field strength measurementsof various CdTe sensors The exponential function accountsfor the compression of electric field lines close to the pixelelectrodes

Guni et al [27] have investigated charge sharing andenergy resolution of CdTe sensors for various pixel sizes con-nected to the photon counting pixel detectorMedipix2 Basedon their study a Monte-Carlo simulation was developed thatreproduced the energy deposition spectra for X-ray photonson the analog side of the pixel electronics [28] In order totake charge carrier diffusion into account the locations of the


electrons arriving after drift at the pixel electrode plane weredetermined according to a Gaussian probability distributiondepending on their drift timeThe width of the Gaussian wascalculated with the model presented by Spieler and Haller[29] adapted to the charge carrier transport properties ofCdTe The charge induced by each drifting charge carrier inthe pixel electrode was calculated using the Shockley-Ramotheorem [30 31] which describes the calculation of currentsinduced in an electrode by a moving charge The integral ofthe induced current over time is the induced charge 119876 =

119902Δ120593 where Δ120593 is the difference of the weighting potentialvalues of the starting point and the end point of the chargecarrier trajectory and 119902 is the charge of the charge carrierTheweighting potential 120593( 119903) for a certain geometry of electrodesis the solution of the Laplace equation nabla

2120593( 119903) = 0 with the

boundary conditions that the weighting potential equals 1at the sensing electrode and 0 at the positions of all otherelectrodes [32] In the pixel detector the weighting potentialis 1 at the pixel electrode (anode) and 0 at the commonelectrode (cathode) The weighting potential was calculatedfor each combination of sensor thickness and pixel pitchwith the model presented by Castoldi et al [26] Figure 1shows the weighting potentials for different combinationsof thickness and pixel size It can be seen that the largestportion of the signal is induced for electrons close to thepixel electrodes In the simulation the end-point of eachcharge carrier is determined by calculating what is reachedfirst the position after drift at the end of its lifetime theelectrode (anode for electrons or cathode for holes) or theend of the integration time in the preamplifier To calculatethe individual length of life of a charge carrier a randomdistribution according to the life-time of the charge carriertype was usedThe total induced charge of an eventmdashwhich isa measure of the collected energy depositionmdashwas calculatedas the sum of the induced charges of all carriers releasedalong all segments of the track The analog electronics noiseand variations of discriminator threshold among pixels weretaken into account by adding an energy deposition accordingto a Gaussian distribution with a standard deviation of 200electron charges In each pixel the simulated signal wascompared to a discriminator threshold which was set toa realistic value of 7 keV for the simulations of double-beta decays and single electrons If the energy was smallerthan threshold the signal in the pixel was ignored and notprocessed any further In case the threshold was exceededa contribution ΔToT of the time-over-threshold noise wasconverted to energy and added to the collected energy inthe pixel Time-over-threshold noise is mainly due to voltagefluctuations on the falling edge of the preamplifier pulsewhenit comes close to the threshold

222 Energy Resolution in the Pixel To model time-over-threshold noise the energy-deposition 119864 in the pixel wasfirst converted to a time-over-threshold value ToT with thecalibration function ToT(119864) = (119886 times 119864 + 119887) + 119888(119864 minus 119889) 119886119887 119888 and 119889 were derived for each pixel from measurementswith X-ray fluorescence and radioactive sources The firstterm in parentheses describes the linear dependence ofToT on the energy for deposited energies well above the

threshold of the discriminator This behavior is due to thetriangular shape of the voltage pulse at the output of thepreamplifier in the pixel electronics and due to the linearityof the preamplifier pulse height with collected charge Theexact shape of the tip of this pulse has strong influenceon the time-over-threshold measurement if the pulse heightis only slightly above discriminator threshold The shapeof the tip is the result of an interplay between the chargeintegration on the feedback capacitance and the dischargingwith a constant current in the preamplifier circuit The linearrelation between time-over-threshold and collected chargeno longer holds for small amounts of collected charge time-over-threshold becomes shorter than one would expect fromthe behavior at large amounts of collected chargeThe secondterm in ToT(119864) then becomes dominant The applicability ofthis function to describe the energy measurements in time-over-threshold mode with the Timepix was first proved byJakubek [33]

The standard deviation of time-over-threshold measure-ments was determined as a function of time-over-thresholdby injecting test pulses into the input of the preamplifier ofthe Timepix Randomizing a Gaussian distribution centeredat 0 with this standard deviation gives a value ΔToT forthe specific collected energy in the pixel The sum ToT +

ΔToT is then back-projected to the energy-deposition axisaccording to the above-mentioned calibration curve Thusan energy-deposition value is obtained for each pixel in thesimulation including electronics noise time-over-thresholdnoise electron and hole signal limited charge carrier lifetimeweighting potentials drift and diffusion

The full width at half maximum of the full energy peakΔ119864FWHM of photoabsorption was measured by irradiationof the Timepix with X-ray fluorescence and with photonsfrom radioactive decays Figure 2 shows the relative energyresolution Δ119864FWHM119864 as a function of the detected energy119864 for simulation and measurement The relative energyresolution improves with increasing energy due to betteraccuracy of the time-over-thresholdmeasurementThe time-over-threshold of pulses that are well above threshold for alonger time is affected (relatively) less by electronics noiseon the falling edge of the pulse than for shorter pulses Themeasured relative energy resolution Δ119864FWHM119864 in clustersof triggered pixels is 132 at 59 keV 82 at 80 keV and59 at 121 keV detected energy Good agreement is found forsimulated and measured energy resolution values of the fullpixel matrix after pixel-wise time-over-threshold calibrationof the Timepix detector coupled to a 1mm thick CdTelayer with 110 120583m pixel pitch in the X-ray energy rangeThe differences between simulated and measured values ofthe relative energy resolution were smaller than 06 fordetected energies between 59 keV and 121 keV For lowerenergies the simulated energy resolution is worse than theenergy resolution in the measurement The total energyin all triggered pixels was taken as the measured energy-deposition of the event if more than one pixel was triggereddue to charge carrier diffusion or the track length of thephoto- or Compton-electrons Determination of Δ119864FWHM119864

for energies larger than about 121 keV by irradiation withphotons was almost impossible because in this energy range


00001

0001

001

01

1

minus05 0 05 1 15 2 25

110120583m220120583m

330120583m

Distance from pixel electrode (mm)

Wei

ghtin

g po

tent

ial

1e minus 05

(a)

00001

0001

001

01

1

minus02 0 02 04 06 08 1 12

Wei

ghtin

g po

tent

ial

Distance from pixel electrodesensor thickness

2mm3mm

4mm

1e minus 05

1e minus 06

1e minus 07

1e minus 08

(b)

Figure 1 (a)Weighting potential for a 2mm thick CdTe sensor for different pixel pitch as functions of the distance 119911 from the pixel electrodeplane (b) Weighting potential for different sensor thicknesses at fixed pixel pitch of 110 120583m as function of the ratio of the distance from thepixel electrode plane to the sensor thickness Weighting potentials were calculated according to the model of Castoldi et al [26]

0 20 40 60 80 100 120 1400

01

02

03

04

05

06

07

08

09

1

01

MeasurementSimulation

Deposited energy E (keV)

ΔE

FWH

ME

Figure 2 Simulated and measured relative energy resolutionΔ119864FWHM119864 of the Timepix detector with a 1mm thick CdTe sensorand 110120583mpixel pitch in time-over-threshold mode as a function ofdeposited energy 119864 Δ119864FWHM is the full width at half maximum ofthe full-energy peak at energy 119864

the cross-section of the photoelectric effect strongly decreaseswith increasing photon energy

223 Energy Resolution of Tracks The question ariseswhether or not this energy resolution is sufficient for a 0]120573120573-decay search experiment Figure 3 illustrates the double-beta decay imaging chain of a 3mm thick CdTe sensorwith 110 120583m pitch In Figure 3(a) the simulated ldquoimagerdquo ofthe energy deposited in a 0]120573120573-event is shown The colorrepresents energy deposition in keV In Figure 3(b) the imageof the (energy-deposition equivalent) induced signals in thepixel electrodes is presented Figure 3(b) thus shows theappearance of the track in terms of input signal strength to

the amplifier after drift diffusion trapping and inductionFigure 3(c) shows the appearance of the event after in-pixeldiscrimination with a 7 keV threshold It looks similar but isnot identical to the ldquoreal trackrdquo Figure 3(a)

An experiment has been carried out to test the simulationpredictions of the energy resolution for electron tracks andto test a neural network for single-electron identificationThe idea of the experiment was to produce two-charged-particle track structures similar to 0]120573120573-decays in order toassess the energy resolution for the tracks Electron-positrontracks were generated by pair production The experimentand the results were presented by Filipenko et al [20] inmore detail A 1mm thick CdTe sensor layer with ohmiccontacts (Pt) biased continuously at minus500V was exposedfrom the side to 2614MeV photons from the decay of 208TlThe Timepix detector used in this study was assembledby the Freiburger Materialforschungszentrum FMF whichhas also evaluated CdTe as sensor material on Timepixdetectors [19] The setup was not temperature stabilized Dueto the heat dissipation from the ASIC the temperature ofthe CdTe sensor was approximately 37∘C Stabilization ofthe detector at lower temperature is an option for leakagecurrent reduction and possibly for an improvement of theenergy resolution Images in time-over-threshold mode weretaken using the USB readout [34] controlled by the dataacquisition software Pixelman [35] The probability for pairproduction is 162 of the Compton scattering probabilityin CdTe at this photon energy Thus the spectrum ofenergies in tracks was dominated by Compton scatteringThe images have been analyzed for single-electron tracksand electron-positron track pairs with the artificial neuralnetwork FANN [36] The network comprised 10 input unitsand 1 output unit on 5 hidden layers with 200 neurons eachThe activation function tanh(03119909) with the learning methodResilient Propagation produced the best results The neuralnetwork was trained with simulated tracks and was applied


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)

(a) Deposited energy in the geometric volume of eachpixel

minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)

(b) The input to the amplifier in each pixel

minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

Pixel

(c) After discrimination

Figure 3 Example of the appearance of a 0]120573120573-track simulated for a 3mm thick CdTe sensor with a pixel pitch of 110 120583m at different stagesof the imaging chain The x- and y-coordinates give the pixel row and column The color bar gives the deposited or measured (time-over-threshold) energy in keV

to measured data The sum of the energy depositions inall pixels in the tracks has been determined for each trackstructure after removing 120572-particle signatures and muontracks Figure 4 shows the measured spectra of depositedenergies in tracks for pair production and single-electronevents after reconstruction with the neural network wherethe known classification errors of the network have beencorrected for A clear peak frompair production is visibleThecorrected spectrum for single-electron tracks almost showsno relict of a pair-production peak The energy resolution inthe pair production electron-positron tracks wasmeasured tobeΔ119864FWHM119864 = 377whichwas about twice the resolutionthat was expected from simulationThis discrepancy was dueto the extrapolation of the time-over-threshold versus energycalibration curves from the highest photon energy used forcalibration (121 keV) to deposited energies of up to 400 keVin single pixels High-energy photons of several hundred keVcannot be used for energy calibration because of the smallcross-section of the photoelectric effect and the long electrontracks at these energies Photoelectrons of these energies aremostly not confined in one pixel so that for each calibration

event the energy depositions in individual pixels would beunknownNevertheless the results of the experiment showedthat the simulation and the track analysis with the neuralnetwork worked well since the separation between single-electron tracks (blue in Figure 4) and pair-production events(green in Figure 4) was as expected

3 Results and Discussion

31 Simulation Setup All simulations of double-beta decayswere carried out with a geometry where 2 times 2 Timepix detec-tors with CdTe sensors are packed together in contact to eachother Two of such 2 times 2 matrices were placed on top of eachother with their CdTe sensors facing each other With thisarrangement the loss of electrons at the edges was reducedFurthermore electrons which leave the CdTe sensors at thecommon electrodes could deposit their remaining energy inthe opposite CdTe detectorThis increases the 0]120573120573 detectionefficiency

Test measurements [20] have shown that a bias voltageof minus500V was an appropriate choice for the 1mm thick


1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts

MeasurementSingle electrons reconstructedPair production reconstructed

Figure 4 Red reconstructed distribution of measured total energydepositions in tracks of a 1mm thick CdTe Timepix detector with110120583m pixel pitch for irradiation with 2614MeV photons throughits edge Straight line tracks caused by muons and circular trackstructures caused by 120572-particles have been removed before trackanalysis with the artificial neural network Green reconstructedtotal-energy distribution for events that should stem from pairproduction Blue reconstructed total-energy distribution of single-electron tracks

sensor with ohmic contacts The drift times were reasonablyshort the blurring of tracks due to diffusion of chargecarriers was not too strong The leakage current of 08 nAper pixel at a sensor temperature of approximately 37

∘C wasat an acceptable level so that a reasonably low discriminatorthreshold of 55 keV could be realized experimentally with110 120583m pixel pitch The leakage current compensation circuitin each pixel of the Timepix can even compensate for leakagecurrents up to minus10 nA [23] in electron collection mode Evenwith minus700V bias voltage only 13 of the pixels did not workproperly [20] It shall be pointed out that in principle theleakage current could be further reduced either with Schottkycontacts instead of ohmic contacts on the CdTe layer [21] orby cooling the detector which would probably also improveenergy resolution Remoue et al [37] demonstrated that theleakage current of 4 times 4 times 1mm3 CdTe sensors with indiumSchottky contacts operated atminus20∘Cwithminus600V bias voltagecan be smaller than 100 pA This value would correspond toonly 19 pA leakage current per pixel for 550120583m pixel pitchThe analog pixel electronics of the Timepix ASIC can evencompensate for three orders of magnitude stronger leakagecurrents The drawback of Schottky contacts would be thatthe sensor would tend to polarize [21] due to the buildup ofspace charges Polarization in CdTe typically worsens chargecollection efficiency and can be reduced by cooling [38] Theinfluence of the polarization effect could also be overcomeby switching off the bias voltage for some seconds every fewminutes [39] It has already been shown [40] that almostcomplete charge collection can be obtained in 05mm thickCdTe and 2mm thick CZT layers with low bias voltages ofabout minus100V Therefore we assumed for our simulations ofthe performance of a pixel detector for various combinations

0 100 200 300 400 500 600 700 800 900

00001

0001

001

01

Single electron0120573120573

Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08

Figure 5 Probability density 119889119875119889119864 that a triggered pixel in a trackhas collected a certain energy 119864 for neutrinoless double-beta decay(blue) and for single electrons (red) 28MeV total deposited energyin the track was required for both event types

of pixel pitch and sensor thickness that the pixel detectorcan be operated with bias voltages of minus500V per mm sensorthickness

The energy resolution of a single pixel is asymp13 (FWHM)for asymp59 keV energy deposition The question arises whetheror not a sufficient energy resolution for 0]120573120573-decay detectioncan be obtained with this kind of detector

32 Total-Energy Spectra of Double-Beta Decay EventsFigure 5 shows the simulated spectrum of detected energiesin individual pixels caused by 0]120573120573-decays and by singleelectrons for 28MeV energy deposition in all triggered pixelsof an event The spectra were calculated for a 3mm thickCdTe sensor with 110 120583m pixel pitch For 0]120573120573-events mostof the pixels record energies below 100 keV and some pixelscould receive energy deposition of more than 700 keV Insingle-electron events pixels are triggered more likely withsmaller energy-depositions due to the lower ionization den-sity for more energetic electrons Larger energy depositionsoccur with a higher probability in 0]120573120573-events A largefraction of pixels is triggered by small amounts of energy Atlow energies the energy resolution of the Timepix detectorwith its Wilkinson type ADC (time-over-threshold) is notthe best We therefore studied whether or not this hybridpixel detector with time-over-threshold measurement couldachieve sufficient energy resolution for the two-electrontrack structure to obtain sufficient separation between thepeak expected at the full Q-value of the decay (281350 plusmn

013) keV [13] and the high-energy tail of the unavoidable2]120573120573-background The pixel pitch and the thickness of theCdTe sensor layer were the most important free parametersin the design of the pixel detector

Figure 6 shows the spectra of total detected energy for0]120573120573-decay in comparison to the spectrum of the twoelectrons emitted in 2]120573120573-decays in the region of theQ-valuefor four different combinations of pixel size and thicknessof the CdTe layer An effective Majorana neutrino massof 42meV (1198790]

12= 26 times 10

26 yr) and a half-life of


2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05

(a) 2 mm thickness 55 120583m pitch

2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05

(b) 3 mm thickness 110 120583m pitch

2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05

(c) 3 mm thickness 165 120583m pitch

2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05

(d) 5 mm thickness 110 120583m pitch

Figure 6 Simulated spectra of the total energy given in number of events per kgtimeskeVtimesyr for 0]120573120573- (blue) and 2]120573120573-decays (red) Cadmiumwas assumed to be enriched to 90 in 116CdThe green vertical line indicates the position of the Q-value of the decay The shifts of the peakpositions for 0]120573120573-decays to deposited energies smaller than the Q-value is due to charge sharing at the edges of the electron tracks

1198792]12

= 288 times 1019 yr [14] were assumed The simulation

of the 2]120573120573-spectra was carried out separately in intervalsof the sum of emission energies of the two electrons Thereason is that the probability for a 2]120573120573-decay decreases withincreasing sum of the energies of the two electrons in theregion of the Q-value The numbers of detected events as afunction of the total detected energywereweighted accordingto the probability that a 2]120573120573-decay occurs with the sumof energies of the two electrons in the interval This resultsin statistic errors in the simulated 2]120573120573-spectra in Figure 6which decrease with improving energy resolution

We observed that the signal peaks did not appear at theQ-value of 2814MeV but at a smaller energy 119864

119876= 119876minusΔ119864shift

depending on bias voltage pixel size and sensor thicknessThis loss of total energy is mainly due to the loss of chargefrom each triggered pixel to under-threshold neighboringpixels The loss of charge is mainly due to diffusion ofcharge carriers during drift towards the pixel electrodes Theaverage energy loss Δ119864shift in the signal is about 70 keV for

the configuration with best energy resolution The distancebetween the signal peak and the Q-value increases withincreasing sensor thickness decreasing bias voltage anddecreasing pixel size The same effect shifts the spectrum ofelectron energies from 2]120573120573-decays towards lower energiesFor a 3mm thick sensor layer with 165120583m pixel pitch thecontribution of the 2]120573120573-decay channel to the number ofaccepted events would be only about 16 Here we assumedan effectiveMajorana neutrinomass of119898

120573120573= 42meV and an

acceptance window width for signal events of Δ119864cut = 59 keVcentered at 2738 keV

33 Total-Energy Resolution 2000 neutrinoless double-betadecay events with random electron momenta and positionsin the pixel matrix were simulated to determine the energyresolution for each combination of pixel pitch and sen-sor layer thickness Figure 7 shows the energy resolutionΔ119864FWHM(119864

119876)119864119876of the two-electron track signature at 119864

119876

as functions of the pixel pitch for different values of the


1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()

Pixel pitch (120583m)

2mm3mm

4mm5mm

Figure 7 Simulated relative energy resolution Δ119864FWHM(119864Q)119864Q forvarious combinations of pixel pitch and sensor thickness

sensor thickness for bias voltages of minus500V per mm sensorthickness Such good energy resolutions can be achievedbecause the errors made in each pixel by the time-over-threshold measurement average out to a certain extent inthe track Total-energy resolution of the tracks improveswith decreasing pixel pitch (increasing number of triggeredpixels) unless the losses of energy underneath discriminatorthresholds become significant If smaller pixels are used thenumber of pixels at the edge of the track is larger and theloss of charges to untriggered pixels adjacent to the triggeredpixels becomes larger The collected energy then dependsstrongly on the exact trajectories with respect to the bordersof the pixels Thus the energy resolution for the tracks isworse if pixels are too small A similar argument can beapplied if the sensor is too thick

For 0]120573120573-tracks the best energy resolution of aboutΔ119864FWHM(119864

119876)119864119876

= 131 in the sum electron energywas achieved with a 2mm thick CdTe sensor layer with220120583m pixel size at a bias voltage of minus500V per mm sensorthickness The sensor thickness pixel size combinations((3mm 330 120583m) and (4mm 440 120583m)) showed only slightlyworse energy resolutions

34 Sensor Thickness So far the detection efficiency has notbeen considered Thicker sensor layers have the advantagethat less pixels are necessary to reach a certain mass of CdTeand therefore a certain sensitivity to the effective Majorananeutrinomass A thicker sensor has several other advantagesincreased volume-to-surface ratio and thus reduced specificbackground rate from surfaces reduced total static powerconsumption of the analog pixel electronic cells reducednecessary number of events for pixel calibration and reducedbump-bonding costs The fraction of the tracks that are fullycontained in the sensor increases with sensor thickness Onthe other hand energy resolution for tracks eventually wors-enswith increasing sensor thickness because of the increasinginfluence of charge splitting (charge sharing) between pixelsFigure 8 presents the simulated half-life sensitivity accordingto the unified approachmdashwhich is presented in [41]mdashfor aconfidence level of 90 after 5 years of measuring time with

0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm

Figure 8 Simulated half-life sensitivity of a 420 kg CdTe pixeldetector experiment (Cd enriched to 90 in 116Cd) for variouscombinations of pixel pitch and sensor thickness Backgroundsources other than 2]120573120573-decays were neglected at this stage

420 kg CdTe (90 116Cd) in the face-to-face setup of pixeldetectors In terms of sensitivity the best choice would be asensor which is thicker than 2mm although the best total-energy resolution was found for the configuration (2mm220120583m) At this stage of the analysis the best sensitivitieswere obtained with a 4mm thick sensor with 330 120583m pixelsize or with a 5mm thich sensor with 440 120583m pixel size Thesimulated half-life sensitivity for 3mm thickness and 165 120583mpixel size is very close to the half-life sensitivities of theconfigurations ((4mm 330 120583m) and (5mm 440 120583m)) It canalso be seen that the simulated half-life sensitivity does notstrongly depend on the pixel size for 3mm thickness between165 120583m and 220120583m For calculation of the sensitivities inFigure 8 only background from 2]120573120573-decays was taken intoaccount in the region of 119864

119876 In an experiment background

like electrons from the decay of 214Bi Compton scatteredelectrons and 120572-particles would also be present It can beexpected that discrimination of signal and single-electronbackground by analysis of the track topology ismore effectivewith smaller pixel sizes Track resolution is worse with thickersensor layers because of charge sharing Thicker sensorsand a larger pixel pixel thus complicate the backgroundrejection with track analysis Therefore the combination ofa 3mm CdTe layer thickness with a pixel size of 165 120583mseems to be the optimal compromise for a pixel detector Thedetection efficiency for 0]120573120573-decay events with this optimalconfiguration is 559

35 0]120573120573- and Single-Electron Tracks The main motivationfor employing pixel detectors in the search for neutrinolessdouble-beta decay is their ability to visualize tracks Trackanalysis shall be used to discriminate background eventsFor example electrons or positrons of sufficient energy canemerge from beta decays from radioactive contaminantseither present in the CdTe sensor the bump-bond materialthe electrode metals the ASIC the readout electronicsclose to the CdTe sensors the shielding or the support


structures 214Bi for example undergoes beta decay with aQ-value of 33MeV which is above theQ-value of the double-beta decay of 116Cd High-energy background electrons canalso be released by Compton scattering in the sensor orsurrounding parts by high-energy photons Such photonscan be generated for example in 120574-120574-cascades after thermalneutron capture 113Cd(119899 120574)114Cd of 113Cd remnants with avery large cross-section

Figure 9 shows the appearance of an example of a 0]120573120573-decay event in pixel matrices with differing pitch rangingfrom 55 120583m to 880 120583m to illustrate the influence of pixel pitchon track resolution

Figure 10 shows examples of images of simulated energydepositions in the pixel matrix for ldquoobviousrdquo Figure 10(a)and ldquodeformedrdquo Figure 10(b) 0]120573120573-events for a 3mm thickCdTe sensor with a pixel pitch of 110 120583m at a discriminatorthreshold of 7 keV A bias voltage of minus1500V was appliedThe appearance of the tracks in the image is affected bythe diffusion of charge carriers during their drift electronscattering in the CdTe sensor and noise in the electronicsThe naive picture is that a double-beta decay appears as tworegions with large energy deposition per pixel (Bragg peak)that are connected by a thinner line of pixels One can see inFigure 10(b) that this is not always the case The main reasonis that due to scattering off lattice atoms the electrons canalsomove parallel to the electric field linesThey then deposita large amount of energy in a few neighboring pixels whichlooks like a Bragg-peak region

Figure 11 shows two examples of simulated track imagesof single electrons emerging for example from a beta decayof 214Bi contaminants with a total energy detected by thepixel matrix close to 119864

119876 Comparing these images with the

images of signal events presented in Figure 10 it is obviousthat some of the single-electron tracks will look like the twotracks of two electrons fromdouble-beta decay and vice versa

36 Discrimination of Single-Electron Background We usedrandom decision forests for discrimination between single-electron tracks and double-beta decay event pattern Theconcept of random decision forests is based on the classof decision tree algorithms which are widely used for dataclassification The basic idea of random decision forests hasbeen described byHo [42] Random decision forests typicallyhave an increased ability to generalize They preserve theadvantages of decision trees like a high classification perfor-mance and a very fast execution Random decision forestsuse random feature subspaces to construct multiple decisiontrees which carry out a majority vote The implementation ofthe random decision forest used in this study is based on thelibrary ALGLIB [43] The classification program was trainedwith simulated electron tracks of double-beta decay and withsingle electrons both causing a measured energy close to119864119876in the pixel matrix The cut in the decision process for

identifying an event as signal or background is optimized forthe best sensitivity of the experiment to the effectiveMajorananeutrino mass In the following we describe in detail the 10features that were used in the event classification In Figures12 and 13 we show the probability for obtaining a featurevalue in a certain bin width obtained with simulations of

0]120573120573-decay events and single electrons with a total energydeposition in an acceptance window of 59 keV width around119864Q for a 3mm thick CdTe sensor with 110 120583m pixel pitch at abias voltage of minus1500V

For 0]120573120573-decay events we expect less pixels to be trig-gered on average than for a single electron at the same totalenergyThus the number of triggered pixels (Figure 12(a)) inthe track should give a hintwhether a track structure is causedby a signal or background event

A single electron should lose less energy per pixel atthe beginning of its track and trigger many pixels in asmall region when its energy comes close to the Bragg-peakregion where the collected energy per pixel should be largerTherefore we expect that the center of gravity of the energydeposition pattern is different from the center of gravity ofthe binary track structure In an ldquoidealrdquo double-beta decaywe would expect to see a pattern of two single-electrontracks connected in the pixel with the decaying nucleusWe expect a smaller distance between the energy-weightedand binary center-of-gravity of the track structure than fora single electron The distance 119889 equiv radic( 119903weighted minus 119903binary)

2

(Figure 12(b)) becomes a feature of the classification processwhere 119903weighted is the center of gravity of the energy depositionin the track structure and 119903binary is the center of gravity of thepattern of triggered pixels

The beginning of a single-electron track shouldmdashideallymdashbegin with a thin short structure of triggered pixelswith relatively low energy deposition per pixel In idealdouble-beta decay events such a structure should not bepresent at the ends of the track structure We introducedtwo features in the classification process the total energymeasured in two (Figure 12(c)) or in three (Figure 12(d))adjacent pixels with only one neighboring triggered pixelThe smallest of these energy values is used if several of thesestructures exist in an event We defined that neighboringpixelsmust touch each other and be located either in the samerow or in the same column

As additional features we used the length of a structureat the edge of the track in which each pixel has only onetriggered neighbor which in turn had only one triggeredneighbor and so on Typically these structures are longer forsingle-electron tracks (Figure 12(e))

For 0]120573120573-decay eventswe ideally expect to see twodistantstructures with high energy depositions per pixel (eg gt

250 keV) because of Bethe-Bloch-like energy losses Thuswe defined the maximum distance of pixels in the trackhaving detected energies of more than 250 keV as a feature(Figure 12(f))

A single background electron with a total energy deposi-tion in the region of 119864

119876should deposit less energy per pixel

than an electron from a 0]120573120573-decay because of its higherenergy The number of pixels having measured a total energyof less than 185 keV together with their neighbors became afeature (Figure 13(a)) that gives on average larger values forsingle electrons

We expect ideal single-electron tracks to have a line oftriggered pixels at the beginning of the track Therefore the


minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0

minus2121086420minus2

(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m

Figure 9 Simulated pattern of energy depositions in the pixel matrix for a 0]120573120573-decay event in a 3mm thick CdTe sensor for differentgranularities of the pixel matrix The 119909- and 119910-coordinates give the pixel row and column The color bar encodes the energy depositionmeasured with the time-over-threshold method in keV


minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)

minus2 0 2 6 8 10minus2

0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)

Figure 10 Simulated pattern of energy depositions in the pixel matrix for two examples of 0]120573120573-decay events (a) Clear 0]120573120573-decayappearance (b) event that looks like a single-electron track The 119909- and 119910-coordinates give the pixel row and columnThe color bar encodesthe energy deposition measured with the time-over-threshold method in keV

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)

Figure 11 Simulated pattern of energy depositions in the pixel matrix of single electrons with energy deposition close to 119864119876 (a) Electron that

has an appearance similar to a 0]120573120573-decay event (b) Electron track like it is expected in a naive picture The 119909- and 119910-coordinates give thepixel row and column The color bar encodes the energy deposition measured with the time-over-threshold method in keV

number of segments of the track that appeared as straightlines became a feature (Figure 13(b)) We defined a straightline as follows there must be a pixel (starting point) that hadcollected less than 100 keV energy and the remaining part ofthe track is found mainly in one direction if it is viewed fromthe starting point A valid line was counted if two additionalconditions were met First a triggered pixel (end point) hadto be present that was connected with the starting point by atleast a four-pixel long line of neighboring or diagonal pixelsSecond less than four pixels should be connected to the line(neighbors or diagonal) so that the line was not too broadIf a starting point had more than one valid end point the

end point with the largest distance to the starting point waschosen If one line was identified in the track the startingpoints and end points of further valid lines had to have acertain minimum distance to the lines identified before

Tracks of single electrons often appear as thinner tracksthan 0]120573120573-events In one feature (Figure 13(c)) we countedthe number of pixels which are part of a thin track segmentwhich was defined as a structure where the pixel had only twotriggered neighbors on each side

In an additional feature characterizing the track thickness(Figure 13(d)) we counted the number of pixels which had


0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron

(a) Number of pixels (bin width 1 pixel)

0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in

Center-of-gravity distance (pixels)minus05

0120573120573

Single electron

(b) Center-of-gravity distance (bin width 01 pixel)

minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800

Start energy 2 (keV)

Prob

abili

ty p

er b

in

0120573120573

Single electron

(c) Start energy 2 (bin width 10 keV)

0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in

(d) Start energy 3 (bin width 10 keV)

minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in

Start length (pixels)

0120573120573

Single electron

(e) Start length (bin width 1 pixel)

minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07

High energy distance (pixels)

Prob

abili

ty p

er b

in

0120573120573

Single electron

(f) High energy distance (bin width 1 pixel)

Figure 12 Probabilities per bin for the occurrence of feature values in an event for 0]120573120573-decays and for single electronswith energy depositionaround 119864

119876for a 3mm thick CdTe sensor with 110120583m pixel pitch The bin width is given in the caption of each feature


0

005

01

015

02

025

03

035

04

045

0 5 10 15 20

Low energy area (pixels)

Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus

(a) Low energy area (bin width 1 pixel)

0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in

(b) Number of lines (bin width 1 line)

0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron

(c) Thin track pixels (bin width 1 pixel)

0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012

Thickness of track (pixels)

Prob

abili

ty p

er b

in

0120573120573

Single electron

(d) Thickness of track (bin width 1 pixel)



two triggered neighbors so that the three pixels formed atriangle

Many electrons that enter the sensor from the edges couldbe vetoed during data analysis with very high efficiency byusing the columns and rows at the edges as vetoes Thecollision stopping power of a 28MeV electron in CdTe is1161MeV cm2g [44]which translates to an average depositedenergy of 113 keV in a 165120583m-wide pixel This energy depo-sition is well above the possible discriminator threshold Itwould be favorable to use two adjacent pixel columns or rowsas vetoes because pixels at the edges of the sensor sometimessuffer from increased leakage currents Another possibilitywould be reading the charge signal from a field-formingguard ring at the edges of the sensor Thus fiducializing thesensor volume from the edges is possible and would reducethe single-electron background further

37 Sensitivity to the Effective Majorana Neutrino Mass119898120573120573 The sensitivity of a large-scale experiment based on

hybrid pixel detectors with a total CdTe mass of 420 kg

(Cd enriched to 90 in 116Cd) was determined for differentpixel pitch and sensor thickness combinations Backgroundand efficiency reduction with track analysis was accountedfor 2]120573120573-background and the single-electron backgroundwere taken into account The spectrum of the single-electronbackground was modeled as a flat distribution in the regionof 119864119876 The specific single-electron background rate was a

free parameterThe underlying classification process with therandom decision forests was optimized for a pixel pitch of110 120583m The sensitivity of the setup was determined with theldquosimple andunambiguous statistical reciperdquo [41] of the unifiedapproach based on the Feldman-Cousins algorithm [45]Wederived half-life sensitivities for a confidence level of 90reached after 5 years of measurement

The cut width Δ119864cut on the deposited energy sum (forcounting the number of signal events) in the track structurearound 119864

119876was optimized for maximum sensitivity for each

combination of pixel pitch and sensor thickness Figure 14gives the results of this complex optimization It can beseen that the best overall performance over a wide range of


0

1

2

3

4

5

6

00001 0001 001 01 1

b in counts(kg keV yr)

Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness

Figure 14 Simulated half-life sensitivity according to the unified approach [41] for 90 confidence level after 5 years of measuring time with420 kg CdTe employing background identification for different combinations of sensor thickness and pixel size as functions of the specificsingle-electron background rate 119887

background rates can be achieved with a 3mm thick CdTesensor layer and pixel pitch between 165 120583m and 220120583m At abackground level of 119887 = 0001 counts(kgtimes keVtimes yr) the besthalf-life sensitivity of 134 times 10

26 yr is obtained for a 3mmthick sensor with 220120583mpixel sizeThis sensitivity is close tothe half-life sensitivity of 130 times 10

26 yr obtained for the samesensor thickness but with 165 120583m pixel size In our opinion apixel pitch of 165 120583m should be chosen in the experiment inorder to obtain the better resolution of track structures

Figure 15 shows the relative reduction Δ119878(119887)119878(119887) of thesignal and of the electron backgroundΔ119861119861(119887) achieved withthe track analysis The signal 119878 was defined as the numberof detected 0]120573120573-decay events in the signal acceptancewindow around 119864

119876 The background 119861 was the correspond-

ing number of detected electron background events in theacceptancewindow 119887 is the specific background rate (given incounts(kg times keV times yr)) of single electrons before applicationof the random decision forests The higher the backgroundthe more restrictively the classification programs reacted

Thus the detection efficiency was reduced more at higherbackground rates For 3mm thick sensors with 110 120583m pixelpitch the detection efficiency amounted to 55 before eventclassification with the random decision forests A reductionof the detection efficiency of about 23 occurred at abackground level of about 10minus3 counts(kgtimeskeVtimes yr) so thata detection efficiency of 42 was reached after classificationAt the same time the electron background was reduced by75

The net benefit of track analysis could be represented byan effective background reduction factor 119903 which we definedas

119903 =119887RDF119887noRDF

(2)

119887RDF and 119887noRDF were the maximum allowed single-electronspecific background rates 119887 to reach an effective Majorananeutrino mass sensitivity

120573120573with (RDF) and without

(noRDF) event classification in 0]120573120573-decays and single


0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1

b in counts(kg keV yr)1e minus 05

Figure 15 Relative reduction of the number of detected signalevents Δ119878(119887)119878(119887) and the number of single-electron backgroundevents Δ119861119861(119887) in the acceptance window as functions of the orig-inal specific single-electron background rate (given in counts(kg times

keV times yr)) for a 3mm thick CdTe sensor with 165 120583m pixel pitchachieved with the random decision forest

0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r


2D pixel detector3D voxel detector

Figure 16The effective background reduction factor 119903 as a functionof pixel pitch after the classification working only in the sensorplane (red) for a 3mm thick CdTe sensor Additionally the effectivebackground reduction factor 119903 obtained with 3D-track analysis at110120583m pixel pitch is shown (blue)

electrons by the random decision forests For 119887noRDF thecut on the 0]120573120573 total energy peak (window-width Δ119864cutand position) was optimized for maximum sensitivity tothe effective Majorana neutrino mass The random decisionforest was not applied to discriminate between 0]120573120573- andsingle-electron tracks For 119887RDF the random decision forestadditionally classified events and rejected background eventsat the expense of signal efficiency 119903 gt 1 means that alarger single-electron background rate in the experimentcan be tolerated with event classification by the randomdecision forest compared to the same experimental setupwithout using the random decision forest Thus 119903 reflectsthe potential of the event classification with the randomdecision forest with respect to the allowed background rate

119903 measures by how much the background rate needs tobe reduced without performing background rejection withthe random decision forest so that the same sensitivity tothe effective Majorana neutrino mass can be achieved aswith background rejection with the random decision forestThe classification of events with the random decision forestduring data analysis effectively reduces the single-electronbackground to 119887noRDF119903

We used the definition of the effective Majorana neutrinomass sensitivity

120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)

which is an appropriate definition for large background levels1198702is a constant that depends only on the isotope 120576 is the

corresponding detection efficiency 119872 is the total mass ofthe double-beta decay nuclei in the detector 119887 is the single-electron specific background rate in counts(kg times keV times yr)and 119905 is the measuring time Δ119864cut specifies the acceptancewindow width around the 0]120573120573-decay peak in the spectrumof total energies

Figure 16 shows the effective background reduction factor119903 as a function of pixel pitch for a 3mm thick CdTe sensorlayer It can be seen that the track analysis has a greater benefitin an experiment with smaller pixel pitch and that almostno benefit with track analysis can be achieved for pixel sizeslarger than 440 120583m One can see that the exploitation of thetracking properties of a detector with a pixel pitch of 165 120583mreduces the single-electron background level by a factor of22 The sensitivity to the effective Majorana neutrino mass isthus improved by a factor of 122 for the optimal sensor layerconfiguration (3mm thickness 165120583m pitch)

Figure 17 shows the expected sensitivity in terms of effec-tive Majorana neutrino mass of a 420 kg CdTe experimentafter 5 years of measuring time for the optimal sensorconfiguration with track analysis as a function of the single-electron background rate 119887 before event classification in theregion of 119864

119876 2]120573120573-background was taken into account Our

simulations showed that a single-electron background levelof about 2 times 10

minus4 in the region of 119864119876would be necessary to

access the effective Majorana neutrino masses in the invertedhierarchy rangemdashwhich begins at 119898

120573120573asymp 50meVmdashin 5 years

of measuring time at 90 confidence level

38 Discrimination of 120572-Particle Background Figure 18shows a measured ldquotrackrdquo of an 120572-particle with 55MeVki-netic energy impinging on the common electrode sideWith its approximate radial symmetry and high energydeposition in the center it looks completely different to themajority of the 0]120573120573-tracks The track lengths of 120572-particleswith energies close to the Q-value of the 0]120573120573-decay arevery short in CdTe (few micrometers) compared to thesum of the track lengths of the two 0]120573120573-electrons (severalhundred micrometers) and compared to the pixel pitchesunder investigation Thus we can assume in the simulationof 120572-particle signatures that the kinetic energy is depositedat one point The dynamics of the very dense chargecarrier distribution along the short track of an 120572-particle


10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1


Figure 17 Expected sensitivity to the effective Majorana neutrinomass119898

120573120573for the optimal configuration (3mm thickness and 165 120583m

pixel pitch) as a function of the specific single-electron backgroundrate 119887 before track analysis given in counts(kg times keV times yr)

immediately after impact of the particle is complicatedbecause of space charge buildup which partly compensatesthe electric drift field This leads to a period of diffusionwithout significant drift during the early history of thedetection process Additionally charge carrier repulsiontakes place The result is that the pattern of triggered pixelsbecomes larger than one would expect An experiment witha 1mm thick CdTe sensor with 110 120583m pixel pitch revealedthat 20ndash60 pixels are triggered by impacts of 55MeV 120572-particles depending on the bias voltage which was variedbetween minus100V and minus500V We introduced a factor intothe simulation which broadened the distribution of driftedcharge carriers We chose a large range for this value in thesimulation so that the measured distributions of clustersizes for the 55MeV 120572-particles were covered widely withthe simulations for the different bias voltages We thensimulated signatures of 28MeV energy depositionsmdashwhichwere supposed to be caused by 120572-particle impact on thecommon electrode sidemdashfor the whole range of this factor tocover all possible pattern sizes We simulated 10

6120572-particle

impacts with a value for this factor which leads to 120572-particlesignatures that were most difficult to discriminate withthe classification software For this worst case the randomdecision forest trained with simulated pattern of 120572-particleswas able to reject all simulated 120572-particle impacts with lessthan 26 loss of signal events (0]120573120573) We expect that the120572-particle background can be reduced further because theclassification algorithm did not have features dedicated to120572-particle identification (like symmetry of the topologicalpattern with the largest energy deposition in the center)

4 Future Perspectives

41 Tracking in Three Dimensions The analysis presentedso far only used two-dimensional projections of the energydeposition in the electron tracks for background discrimina-tion although an electron travels through the sensor in threedimensions A long track segment of an electron through apixel parallel to the axis of the electric field lines (119911-axis)

99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY

Figure 18 Measured image of the energy deposition of a 58MeV120572-particle impact on the common electrode side recorded with a110120583m pixel pitch Timepix detector with a 1mm thick sensor layer

causes large energy deposition similar to a less energeticelectron travelling perpendicular to the electric field linesAs a consequence of this some single-electron tracks aredifficult to distinguish from signal eventsThis problem couldbe overcome if a 3D tracking hybrid pixel detector wouldbe available Information about the z-components of a trackcould in principle be obtained by measuring differencesin drift times of charge carrier distributions collected byneighboring pixels Campbell et al [46] have proposed aschematic of such an architecture of a pixel detector whichavoids the distribution of a fast clock signal for timingmeasurements to all pixels A fast clock signal supplied toall pixels typically generates noise that in turn deterioratesenergy resolution and increases the minimum discriminatorthreshold Another possibility for an architecture would bethe combination of a coarse time stamp generated by a slowclock signal distributed to all pixels in the matrix and aprecise time stamp generated by a fast oscillator in each pixelThis architecture is implemented in the Timepix3 detector[16]

We have carried out simulations to demonstrate thepotential of 3D tracking with the assumption that a positionresolution of 110 120583m could be achieved in each pixel cellalso in the drift direction This means that 27 ns resolutionof drift time measurements is needed This does not seemto be impossible because the clock cycle spacing of the fastoscillator signal in the Timepix3 is 16 ns The preamplifierpeaking time in the Timepix3 is less than 20 ns and thetime over threshold is provided so that time walk correctionscan be carried out The electron drift time to cross thecomplete sensor thickness of 3mm is 735 ns for a bias voltagedifference of minus1500V As a simple test of 3D track analysis weapplied the two-dimensional track analysis presented abovethree times for each plane in the sensor (119909-119910 119909-119911 119910-119911) independently from each other The result expressed bythe equivalent background reduction factor 119903 is shown inFigure 15 (blue) One can see that with a 3D voxel detector anincrease of the sensitivity to the effective Majorana neutrinomass by a factor of about 161 with track analysis could be


realized This would be a significant improvement comparedto the 2D pixel detector We expect an even stronger increaseof the sensitivity to the effective Majorana neutrino massby analysis of additional topological features which take thethree-dimensional structure into account

42 Improvement of Energy Resolution Energy resolutionshould be further improved In contrast to photon count-ing X-ray imaging or accelerator-based high-energy-physicsexperiments an analog read-out of the energy signal ofpixels with external ADCs is possible in low-backgroundexperiments because of the low overall detection rate It hasbeen demonstrated [47] that an excellent average single-pixelenergy resolution of Δ119864FWHM119864 = 12 at 595 keV canbe achieved with the hybrid pixel detector HEXITEC with250120583m pixel pitch bump-bonded to a 1mm thick CdTe layerwith Schottky contacts biased to minus500V Seller et al [21]reported an energy resolution better than 25 (FWHM) at595 keV on a 2mm thick 20 times 20 pixel CdZnTe detector with250120583mpixel pitch connected to anASICwith a pixel circuitryidentical to the HEXITEC In the HEXITEC detector theenergy signal is digitized externally with a low-noise ADCThe drawback of this pixel detector is that no differences ofdrift times can be obtained The HEXITEC detector lackstime resolution on a few-nanosecond scale which is providedby the Timepix detector Such a time resolution seems tobe necessary in order to be sure that potential double-betadecay events that come from one single decay are not dueto a random coincidence of two single beta decays Timeresolution will already be improved with the Timepix3 activepixel detector Each 55times55 120583m2 pixel of theTimepix3 detector[16] features an amplifier with less than 20 ns peaking time Afast oscillator in each pixel provides a clock pulse each 16 nsfor in-pixel time stamping if the signal pulse height is abovediscriminator threshold In our opinion an analog-electronicspixel architecture feeding an analog read-out chain withexternal low-noise ADCs (like in the HEXITEC detector)should be combined with a fast timing circuit in each pixel(like in the Timepix3) This combination of a fast and a slowcircuit might require the generation of two signal copies onthe pixel level The Medipix3 [48] detector already featuressuch a circuit in each pixel which generates four copies of theamplified sensor signal for reallocation of the charge which issplit between neighboring pixels

5 Conclusion

We have evaluated the sensitivity of an experiment based onpixel detectors connected to pixelated sensors with 420 kg ofCdTe (Cd enriched to 90 in 116Cd) arranged in face-to-face geometry of assemblies (8 cm2 area) for themeasurementof the effective Majorana neutrino mass For the timemdashandenergymdashresolving hybrid pixel detector Timepix we foundan optimal thickness of the sensor layer of 3mm and a pixelpitch of 165120583m With the mass density of enriched CdTe ofapproximately 59 gcm3 this translates to a sensor area of2 times 119m2 with about 875 million pixels We found that 120572-particle background was reduced by at least about 6 orders of

magnitude due to the different track structures of 120572-particlesand electrons

We found that the single-electron background ratecould be reduced with track analysis by about 75 ata single-electron background level of 10minus3 counts(kgtimeskeVtimes

yr) Track analysis with random decision forests reducedthe effective single-electron background by a factor of 22This corresponds to an improvement of the Majorana masssensitivity by a factor of 122 A Majorana mass sensitivity of59meV on a 90 confidence level according to the unifiedapproach [41] might be reached after 5 years of measuringtime for a specific single-electron background rate of 10

minus3

counts(kgtimeskeVtimesyr) In our opinion further improvementsin sensitivity can be achieved with external digitization of theenergy signal instead of the current in-pixel conversion basedon the time-over-threshold method

Currently gaseous detectors outperform the backgroundidentification potential of the semiconductor pixel detectorconcept for 0]120573120573-decay detection because of themuch longertrack length and their possibility of 3D track reconstructionIt was shown within the framework of the NEXT experi-ment [49] that background can be reduced by 3 orders ofmagnitude with tolerable reduction of the signal detectionefficiency by analysis of tracks in a high-pressure XenonTPC Further improvement of the sensitivity to 119898

120573120573with

CdTe pixel detectors will be achieved with track analysisexploiting features of the three-dimensional electron tracksif precise timing measurements of drift time differencesbetween adjacent pixels allow 3D reconstruction of electrontracks

Acknowledgments

The authors cordially thank the COBRA collaboration forintense research on CdTe and CZT detectors and forsupporting this study of the pixel detector option Theythank the Medipix collaboration for the support and forthe development of the Timepix detector They thankthe Deutsche Forschungsgemeinschaft DFG for supportingThomas Gleixner in the project MI 15071-1

References

[1] J Schechter and J W F Valle ldquoNeutrinoless double-decay inSU(2) times U(1) theoriesrdquo Physical Review D vol 25 no 11 pp2951ndash2954 1982

[2] H Nunokawa W J C Teves and R Z Funchal ldquoConstrainingthe absolute neutrino mass scale and Majorana CP violatingphases by future neutrinoless double beta decay experimentsrdquoPhysical Review D vol 66 no 9 Article ID 093010 2002

[3] R Arnold C Augier J Baker et al ldquoProbing new physicsmodels of neutrinoless double beta decay with SuperNEMOrdquoEuropean Physical Journal C vol 70 no 4 pp 927ndash943 2010

[4] J J Gomez-Cadenas J Martın-Albo MMezzetto F Monrabaland M Sorel ldquoThe search for neutrinoless double beta decayrdquoRivista del Nuovo Cimento vol 35 no 2 pp 29ndash98 2012

[5] The NEXT Collaboration ldquoInitial results of NEXT-DEMO alarge-scale prototype for the NEXT-100 experimentrdquo Journal ofInstrumentation vol 8 Article ID P04002 2013


[6] S Sch119894nert I Abt M Altmann et al ldquoThe GERmanium De-tector Array (GERDA) for the search of neutrinoless 2120573 decaysof 76Ge at LNGSrdquoNuclear Physics B vol 145 pp 242ndash245 2005

[7] D G Phillips II D G Phillips II E Aguayo et al ldquoTheMajorana experiment an ultra-low background search forneutrinoless double-beta decayrdquo Journal of Physics ConferenceSeries vol 381 conference 1 Article ID 012044

[8] K Zuber ldquoCOBRAmdashdouble beta decay searches using CdTedetectorsrdquo Physics Letters B vol 519 no 1-2 pp 1ndash7 2001

[9] J Ebert M Fritts C Goszligling et al ldquoCurrent status andperspectives of the COBRA experimentrdquo Advances in HighEnergy Physics vol 2013 Article ID 703572 6 pages 2013

[10] P Cermak I Stekl V Bocarov et al ldquoBackground capabilitiesof pixel detectors for double beta decaymeasurementsrdquoNuclearInstruments and Methods in Physics Research A vol 633 no 1pp S210ndashS211 2011

[11] P Cermak I Stekl Y A Shitov et al ldquoUse of silicon pixeldetectors in double electron capture experimentsrdquo Journal ofInstrumentation vol 6 no 1 Article ID C01057 2011

[12] J Suhonen and O Civitarese ldquoWeak-interaction and nuclear-structure aspects of nuclear double beta decayrdquo Physics Reportvol 300 no 3-4 pp 123ndash214 1998

[13] K Zuber ldquoNeutrinoless double beta decayrdquo Pramana Journal ofPhysics vol 79 pp 781ndash791 2012

[14] Mathieu Bongrand for the NEMO-3 Collaboration ldquoResultsof the NEMO-3 double betadecay experimentrdquo httparxivorgabs11052435

[15] F A Danevich A S Georgadze V V Kobychev et al ldquoSearchfor 2120573 decay of cadmium and tungsten isotopes final resultsof the Solotvina experimentrdquo Physical Review C vol 68 no 3Article ID 035501 12 pages 2003

[16] V Gromov M van Beuzekom R Kluit et al ldquoDevelopmentand applications of the Timepix3 readout chiprdquo in Proceedingsof 20th Anniversary International Workshop on Vertex detectorsPoS (Vertex 2011) 046 Rust Austria June 2011

[17] X Llopart R Ballabriga M Campbell L Tlustos and WWong ldquoTimepix a 65k programmable pixel readout chip forarrival time energy andor photon counting measurementsrdquoNuclear Instruments andMethods in Physics Research A vol 581no 1-2 pp 485ndash494 2007

[18] M Campbell ldquo10 years of the Medipix2 collaborationrdquo NuclearInstruments and Methods in Physics Research A vol 633 no 1pp S1ndashS10 2011

[19] D Greiffenberg A Fauler A Zwerger andM Fiederle ldquoEnergyresolution and transport properties of CdTe-Timepix-assem-bliesrdquo Journal of Instrumentation vol 6 no 1 Article IDC010582011

[20] M Filipenko T Gleixner G Anton J Durst and T MichelldquoCharacterization of the energy resolution and the trackingcapabilities of a hybrid pixel detector with CdTe-sensor layer fora possible use in a neutrinoless double beta decay experimentrdquoThe European Physical Journal C vol 73 article 2374 2013

[21] P Seller S Bell R J Cernik et al ldquoPixellated Cd(Zn)Te high-energy X-ray instrumentrdquo Journal of Instrumentation vol 6 no12 Article ID C12009 2011

[22] H Spieler Semiconductor Detector Systems Oxford SciencePublications 2005

[23] X L Cudie Design and characterization of 64K pixels chipsworking in single photon processing mode [PhD thesis] Depart-ment of Information Technology and Media Mid SwedenUniversity

[24] O A Ponkratenko V I Tretyak and Y G Zdesenko ldquoEventgenerator DECAY4 for simulating double-beta processes anddecays of radioactive nucleirdquo Physics of Atomic Nuclei vol 63no 7 pp 1282ndash1287 2000

[25] J Giersch A Weidemann and G Anton ldquoROSImdashan object-oriented and parallel-computing Monte Carlo simulation forX-ray imagingrdquo Nuclear Instruments and Methods in PhysicsResearch A vol 509 no 1ndash3 pp 151ndash156 2003

[26] A Castoldi E Gatti and P Rehak ldquoThree-dimensional analyt-ical solution of the laplace equation suitable for semiconductordetector designrdquo IEEE Transactions on Nuclear Science vol 43no 1 pp 256ndash265 1996

[27] E Guni J Durst B Kreisler et al ldquoThe influence of pixelpitch and electrode pad size on the spectroscopic performanceof a photon counting pixel detector with CdTe sensorrdquo IEEETransactions on Nuclear Science vol 58 no 1 pp 17ndash25 2011

[28] EGuni J Durst TMichel andGAnton ldquoMaterial reconstruc-tion with the Medipix2 detector with CdTe sensorrdquo Journal ofInstrumentation vol 6 no 1 Article ID C01037 2011

[29] H Spieler and E Haller ldquoAssessment of present and futurelarge-scale semiconductor detector systemsrdquo IEEE Transactionson Nuclear Science vol 32 no 1 pp 419ndash426 1985

[30] W Shockley ldquoCurrents to conductors induced by a movingpoint chargerdquo Journal of Applied Physics vol 9 no 10 pp 635ndash636 1938

[31] S Ramo ldquoCurrents induced by electron motionrdquo Proceedings ofthe IRE vol 27 pp 584ndash585 1939

[32] G Knoll Radiation Detection and Measurement John Wiley ampSons New York NY USA 4th edition 2010

[33] J Jakubek ldquoPrecise energy calibration of pixel detector workingin time-over-threshold moderdquo Nuclear Instruments and Meth-ods in Physics Research A vol 633 no 1 pp S262ndashS266 2011

[34] M Platkevic V Bocarov J Jakubek S Pospisil V Tichy andZ Vykydal ldquoSignal processor controlled USB20 interface forMedipix2 detectorrdquoNuclear Instruments andMethods in PhysicsResearch A vol 591 no 1 pp 245ndash247 2008

[35] T Holy J Jakubek S Pospisil J Uher D Vavrik and ZVykydal ldquoData acquisition and processing software package forMedipix2rdquoNuclear Instruments andMethods in Physics ResearchA vol 563 no 1 pp 254ndash258 2006

[36] S Nissen Implementation of a Fast Artificial Neural NetworkLibrary (FANN) Department of Computer Science Universityof Copenhagen (DIKU) 2003

[37] N Remoue D Barret O Godet and P Mandrou ldquoExtensivetesting of Schottky CdTe detectors for the ECLAIRs X-gamma-ray camera on board the SVOM missionrdquo Nuclear InstrumentsandMethods in Physics ResearchA vol 618 no 1ndash3 pp 199ndash2082010

[38] S del Sordo L Abbene E Caroli AMMancini A Zappettiniand P Ubertini ldquoProgress in the development of CdTe andCdZnTe semiconductor radiation detectors for astrophysicaland medical applicationsrdquo Sensors vol 9 no 5 pp 3491ndash35262009

[39] T Seino and I Takahashi ldquoCdTe detector characteristics at 30∘Cand 35∘C when using the periodic bias reset techniquerdquo IEEETransactions onNuclear Science vol 54 no 4 pp 777ndash781 2007

[40] J Fink H Kruger P Lodomez and N Wermes ldquoCharacteriza-tion of charge collection in CdTe and CZT using the transientcurrent techniquerdquoNuclear Instruments and Methods in PhysicsResearch A vol 560 no 2 pp 435ndash443 2006


[41] J J Gomez-Cadenas J Martın-Albo M Sorel et al ldquoSenseand sensitivity of double beta decay experimentsrdquo Journal ofCosmology and Astroparticle Physics vol 2011 no 6 article 0072011

[42] T K Ho ldquoRandom decision forestsrdquo in Proceedings of the 3rdInternational Conference on Document Analysis and Recogni-tion pp 278ndash282 1995

[43] ALGLIB Project (Free edition) Nizhny Novgorod RussianFederation httpwwwalglibnet

[44] National Institute of Standards and Technology ldquoStoppingpower and range tables for electronsrdquo httpphysicsnistgovPhysRefDataStarTextESTARhtml

[45] G J Feldman and R D Cousins ldquoUnified approach to theclassical statistical analysis of small signalsrdquo Physical Review Dvol 57 no 7 pp 3873ndash3889 1998

[46] M Campbell J Jakubek and TMichel ldquoA single layer 3D track-ing semiconductor detectorrdquo Patent applicationWO 2013041114A1 2011

[47] M C Veale S J Bell P Seller M DWilson and V KachkanovldquoX-ray micro-beam characterization of a small pixel spectro-scopic CdTe detectorrdquo Journal of Instrumentation vol 7 ArticleID P07017 2012

[48] R BallabrigaMCampbell EHeijne X Llopart L Tlustos andWWong ldquoMedipix3 a 64 k pixel detector readout chipworkingin single photon counting mode with improved spectrometricperformancerdquo Nuclear Instruments and Methods in PhysicsResearch A vol 633 no 1 pp S15ndashS18 2011

[49] S Cebrian T Dafni H Gomez et al ldquoPattern recognition of136Xe double beta decay events and background discriminationin a high pressure Xenon TPCrdquo httparxivorgabs13063067

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


from most other reactions that might also release energyin the region of the 119876-value of the double-beta decay twoelectrons start simultaneously at one location and travelthrough the detector materials In contrast to neutrinoaccompanied double-beta decay (2]120573120573) the summed kineticenergies of the two electrons from 0]120573120573-decay equal the totalenergy released in the decay (119876-value) Energy resolutionbackground reduction and mass increase are the keys forimproving sensitivity to the effective Majorana neutrinomass If a detector could be built that is able to ldquoimagerdquo thetwo electrons starting at one location most background par-ticles would be eliminated 120572-particles Compton scatteredelectrons electrons and positrons from beta decays (120573minus 120573+)and muons Beta decays to excited states with subsequentinternal conversion of 120574-line photons could still have a similartrack topology but could be identified because the internalconversion electron has a defined energy

The experiments SuperNEMO [3] and the NeutrinoXenon TPC (NEXT) [4 5] plan to perform tracking withor in gaseous detectors Semiconductor detector materialsmdashwhich can in principle serve as sensor materials in hybridpixel detectorsmdashare used in the experiments GERDA [6]Majorana [7] and COBRA [8] The tracking option withCdTe semiconductor pixel detectors has been evaluated asan additional possible route in the COBRA collaboration[8] The ldquoCurrent status and perspectives of the COBRAexperimentrdquo are described in detail also in this special issueof Advances in High Energy Physics by Fritts et al [9]Background studies with silicon sensor pixel detectors havealready been presented in [10] Hybrid pixel detectors are alsoan interesting option for the still missing direct detection ofneutrino accompanied double electron capture [11]

Hybrid pixel detectors comprise pixelated semiconductorsensor layers for particle detection We are thus restrictedto double-beta decay nuclides of elements which cancompose semiconducting materials The technology ofhybrid pixel detectors with silicon sensors is matureThe development of hybrid pixel detectors connected toGermanium sensors is still ongoing CdTe and Cd(Zn)Te finepitch hybrid pixel detectors have already been developedmainly for X-ray imaging for energies from 3 keV to150 keV The elements cadmium tellurium and zincoffer several isotopes that decay via 120573

minus120573minus 120573+120573+ 120573+EC

ECEC 70Zn 114Cd 116Cd 128Te 130Te 106Cd 64Zn 120Te108Cd 116Cd decays via the neutrino accompanied 120573

minus120573minus-

decay to the ground state of 116Sn with the largestQ-value of 2814MeV in the Cd Te Zn complexThe phase-space factor for the 0]120573120573-decay of 116Cd is1198660](119876120573120573 119885) = 468 times 10

minus14 yrminus1 [12] The matrix element|1198720]| is about 35 [13] but the values given in the literature

vary strongly depending on the calculation model The half-life of the 2]120573120573-decaywasmeasured by Bongrand et al [14] tobe1198792]12

= [288plusmn004 (stat)plusmn016 (syst)]times1019 yr Danevich

et al [15] have set a limit of 1198790]12

= 17 times 1023 yr to the

half-life of the 0]120573120573-decay channelThe COBRA-experiment(Cadmium Zinc Telluride 0-neutrino double-beta ResearchApparatus) proposed by Zuber [8] is located in the GranSasso National Laboratory (LNGS) COBRA focuses on

the possible detection of the 0]120573120573-decay in 116Cd withsemiconducting CdZnTe detectors whereby the cadmiumwill be enriched in the isotope 116Cd The original proposalof Zuber [8] is focused on the use of many monolithic cubicCdZnTe detectors with medium size of a few cm3 Theyare larger in volume than the typical sensor layer of a pixeldetector but smaller than the germanium diodes employedin the GERDA experiment [6] Each CdZnTe crystalsshould be read out individually This option is the mainroute of the COBRA collaboration because experimentalcomplexity and technical challenges are less demandingthan in the case of a large-scale experiment with 420 kgof CdTe pixel detectors Such a large mass is necessaryto access the inverted hierarchy neutrino mass schemewhere 119898

3lt 1198981

lt 1198982 in reasonable measuring time One

additional direction that has been followed in the COBRAstudy was the exploitation of CMOS-based hybrid activepixel detectors with a sensor layer of the II-VI-semiconductorCdTe The idea is that the topological structure of the tracksof the two decay electrons from a 0]120573120573-decay of 116Cdmightbe used to discriminate between 0]120573120573-events and singleelectrons from background processes Possible backgroundprocesses include electrons from beta decays of radioactiveimpurities Compton scattering of high-energetic photonscaused by thermal neutron capture in any remaining 114Cdimpurities or photon production after decays of radioactiveimpurities in the detectors

Hybrid pixel detectors comprise an Application SpecificIntegrated Circuit (ASIC) realized in CMOS technology anda semiconductor sensor layer coupled pixel-wise to the ASICby bump-bonding techniques The ASIC is electronicallysegmented in both a matrix of pixels and a periphery forcontrolling and read-out of the pixel matrix Hybrid pixeldetectors have their origins in high-energy physics and area very important part of the tracking systems in the LHCexperiments In ATLAS CMS and ALICE tracking of high-energy charged particles is performed close to the vertexby detecting the energy depositions of charged particles inseveral layers of pixel detectors with silicon sensor layersIn LHCb hybrid pixel detectors with silicon sensors areused to detect accelerated photoelectrons released fromphotocathodes by Cherenkov photons in the RICH detectorsThe Timepix3 detector [16] which has just been developedby the Medipix collaboration might be a promising optionfor a LHCb particle telescope to replace the current sili-con microstrip system in the SLHC era Can hybrid pixeldetectors also help in neutrino physics experiments to decidewhether the neutrino has Dirac or a Majorana characterBy how much can one reduce the background with trackanalysis

2 Materials and Methods

21 The Timepix Detector The base of this study is the state-of-the-art hybrid active pixel detector Timepix [17] which iscompatible with CdTe sensor layers The Timepix detectorhas been developed by the Medipix collaboration [18] in theframework of the EUDET study It is manufactured with the025 120583mCMOS technology and features a 256 times 256 square
















1sdot 119911 + 119891

2+

1198913sdot 119890minus|119880|sdot119891


1= (580 plusmn 009) times 10



4= (479plusmn






2120593( 119903) = 0 with the









00001

0001

001

01

1

minus05 0 05 1 15 2 25

110120583m220120583m

330120583m


Wei

ghtin

g po

tent

ial

1e minus 05

(a)

00001

0001

001

01

1

minus02 0 02 04 06 08 1 12

Wei

ghtin

g po

tent

ial


2mm3mm

4mm

1e minus 05

1e minus 06

1e minus 07

1e minus 08

(b)


0 20 40 60 80 100 120 1400

01

02

03

04

05

06

07

08

09

1

01



ΔE

FWH

ME







minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

Pixel









1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts





0 100 200 300 400 500 600 700 800 900

00001

0001

001

01


Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08







12= 26 times 10



2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics


















1sdot 119911 + 119891

2+

1198913sdot 119890minus|119880|sdot119891


1= (580 plusmn 009) times 10



4= (479plusmn






2120593( 119903) = 0 with the









00001

0001

001

01

1

minus05 0 05 1 15 2 25

110120583m220120583m

330120583m


Wei

ghtin

g po

tent

ial

1e minus 05

(a)

00001

0001

001

01

1

minus02 0 02 04 06 08 1 12

Wei

ghtin

g po

tent

ial


2mm3mm

4mm

1e minus 05

1e minus 06

1e minus 07

1e minus 08

(b)


0 20 40 60 80 100 120 1400

01

02

03

04

05

06

07

08

09

1

01



ΔE

FWH

ME







minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

Pixel









1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts





0 100 200 300 400 500 600 700 800 900

00001

0001

001

01


Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08







12= 26 times 10



2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






2120593( 119903) = 0 with the









00001

0001

001

01

1

minus05 0 05 1 15 2 25

110120583m220120583m

330120583m


Wei

ghtin

g po

tent

ial

1e minus 05

(a)

00001

0001

001

01

1

minus02 0 02 04 06 08 1 12

Wei

ghtin

g po

tent

ial


2mm3mm

4mm

1e minus 05

1e minus 06

1e minus 07

1e minus 08

(b)


0 20 40 60 80 100 120 1400

01

02

03

04

05

06

07

08

09

1

01



ΔE

FWH

ME







minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

Pixel









1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts





0 100 200 300 400 500 600 700 800 900

00001

0001

001

01


Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08







12= 26 times 10



2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




00001

0001

001

01

1

minus05 0 05 1 15 2 25

110120583m220120583m

330120583m


Wei

ghtin

g po

tent

ial

1e minus 05

(a)

00001

0001

001

01

1

minus02 0 02 04 06 08 1 12

Wei

ghtin

g po

tent

ial


2mm3mm

4mm

1e minus 05

1e minus 06

1e minus 07

1e minus 08

(b)


0 20 40 60 80 100 120 1400

01

02

03

04

05

06

07

08

09

1

01



ΔE

FWH

ME







minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

Pixel









1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts





0 100 200 300 400 500 600 700 800 900

00001

0001

001

01


Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08







12= 26 times 10



2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

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0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

(pixel)


minus2 0 2 4 6 8 10 12 14minus2

0

2

4

6

8

10

12

14

0

50

100

150

200

250

300

350

(pixel)

Pixel









1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts





0 100 200 300 400 500 600 700 800 900

00001

0001

001

01


Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08







12= 26 times 10



2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


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0

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4

6

8

10

12

14

16

0

50

100

150

200

250

300

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el)

(pixel)

(a)

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0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

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014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200minus50

0

50

100

150

200

250

Total energy (keV)

Num

ber o

f eve

nts





0 100 200 300 400 500 600 700 800 900

00001

0001

001

01


Energy (keV)

dPdE

(keV

minus1)

1e minus 05

1e minus 06

1e minus 07

1e minus 08







12= 26 times 10



2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




2600 2650 2700 2750 2800

00001

Sum energy (keV)

Even

ts(k

g keV

yr)

2120573120573

0120573120573

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05


2600 2650 2700 2750 2800

Sum energy (keV)

2120573120573

0120573120573

00001

Even

ts(k

g keV

yr)

0

2e minus 05

4e minus 05

6e minus 05

8e minus 05



1198792]12




119876= 119876minusΔ119864shift



120573120573= 42meV and an




119876



1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




1

2

3

4

5

6

7

0 100 200 300 400 500

Ener

gy re

solu

tion

()


2mm3mm

4mm5mm




119876)119864119876



0

2

4

6

8

10

50 100 150 200 250 300 350 400 450

Hal

f-life

sens

itivi

ty (1

026

yr)


2mm3mm

4mm5mm


















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics















2











minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




minus5 0 5 10 15 20 25 30minus5

0

5

10

15

20

25

30

0

20

40

60

80

100

120

140

160

180

(pixel)

(pix

el)

(a) 55120583m

minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pixel)

(pix

el)

(b) 110 120583m

500

450

400

350

300

250

200

150

100

0

12

10

8

6

4

2

0


(pix

el)

(pixel)

50

(c) 165120583m

minus1 0 1 2 3 4 5 6 7 8 9minus1

0

1

2

3

4

5

6

7

8

9 450

400

350

300

250

200

150

100

50

0

(pixel)

(pix

el)

(d) 220120583m

minus1

0

0

1

1

2

3

4

5

6

7

minus1 2 3 4 5 6 70

100

200

300

400

500

600

700

800

900

(pixel)

(pix

el)

(e) 330120583m

minus05

0

05

1

15

2

25

3

35

minus05 0 05 1 15 2 25 3 350

200

400

600

800

1000

1200

(pixel)

(pix

el)

(f) 880120583m



minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




minus2

0

2

4

6

8

10

12

minus2 0 2 4 6 8 10 120

50

100

150

200

250

300

(pixel)

(pix

el)

(a)


0

2

6

8

10

0

50

100

150

200

250

300

350

400

450

(pixel)

(pix

el)

4

4

(b)


minus2 0 2 4 6 8 10 12 14 16minus2

0

2

4

6

8

10

12

14

16

0

50

100

150

200

250

300

(pix

el)

(pixel)

(a)

minus2 0 2 4 6 8 10 12 14 16 18minus2

0

2

4

6

8

10

12

14

16

18

0

100

200

300

400

500

600

700

800

(pix

el)

(pixel)

(b)








0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0 10 20 30 40 50 60minus001

0

001

002

003

004

005

006

007

008

Prob

abili

ty p

er b

in

Number of pixels

0120573120573

Single electron


0 05 1 15 2 25 3 35 4minus002

0

002

004

006

008

01

012

014

016

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus0005

0

0005

001

0015

002

0025

003

0035

004

0045

0 200 400 600 800


Prob

abili

ty p

er b

in

0120573120573

Single electron


0 200 400 600 800


0120573120573

Single electron

minus0005

0

0005

001

0015

002

0025

003

Prob

abili

ty p

er b

in


minus5 0 5 10 15 20minus01

0

01

02

03

04

05

06

07

Prob

abili

ty p

er b

in


0120573120573

Single electron


minus5 0 5 10 15 20 25 30 35 40minus01

0

01

02

03

04

05

06

07


Prob

abili

ty p

er b

in

0120573120573

Single electron





0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

005

01

015

02

025

03

035

04

045

0 5 10 15 20


Prob

abili

ty p

er b

in

0120573120573

Single electron

005minus


0

01

02

03

04

05

06

07

08

09

1

0 05 1 15 2 25 3

Number of lines

0120573120573

Single electron

Prob

abili

ty p

er b

in


0 2 4 6 8 10 12 14 160

005

01

015

02

025

Thin track pixels

Prob

abili

ty p

er b

in

0120573120573

Single electron


0 5 10 15 20 25 30minus002

0

002

004

006

008

01

012


Prob

abili

ty p

er b

in

0120573120573

Single electron














0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

1

2

3

4

5

6

00001 0001 001 01 1


Hal

f-life

sens

itivi

ty (1

026

yr)

55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(a) 2 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(b) 3 mm thickness

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

1e minus 05

(c) 4 mm thickness

00001 0001 001 01 1


55120583m110120583m165120583m

220120583m330120583m440120583m

0

1

2

3

4

5

6

Hal

f-life

sens

itivi

ty (1

026

yr)

1e minus 05

(d) 5 mm thickness










119903 =119887RDF119887noRDF

(2)





0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

02

04

06

08

1

ΔSSΔBB

ΔSS

ΔBB

00001 0001 001 01 1




0200 400 600 800 1000 12000

1

2

3

4

5

6

7

r







120573120573given in (415) of [41]

120573120573

=1198702

radic120576(119887Δ119864cut119872119905

)

14

(3)













10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




10

100

1000

Sens

itivi

ty to

m120573120573

(meV

)

00001 0001 001 01 1






6120572-particle




99 100 101 102 103 104 105 106 1070

200

400

600

800

1000

1200

1400

1600

76

77

78

79

80

81

82

83

84

Pixel number X

Pixe

l num

berY







5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






5 Conclusion





minus3



120573120573with


Acknowledgments


References

























































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



research article the potential of hybrid pixel detectors...

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