Low-Mass WIMP Sensitivity and Statistical Discrimination of Electron and Nuclear Recoils by Varying Luke-Neganov Phonon Gain in Semiconductor Detectors

0.23 MB·English

by  M. Pyle

JournalofLowTemperaturePhysicsmanuscriptNo.
(willbeinsertedbytheeditor)
M.Pyle1 · D.A.Bauer2 · B.Cabrera1 · J.
Hall2 · R.W.Schnee4 · R.BasuThakur2,3 ·
S.Yellin1
Low-Mass WIMP Sensitivity and Statistical
Discrimination of Electron and Nuclear
Recoils by Varying Luke-Neganov Phonon
Gain in Semiconductor Detectors
2
1
0
January19,2012
2

n
a
Keywords DarkMatter,LowMassWIMP
J
Abstract Amplifyingthephononsignalinasemiconductordarkmatterdetector
8
can be accomplished by operating at high voltage bias and converting the elec-
1
trostaticpotentialenergyintoLuke-Neganovphonons.Thisamplificationmethod

] has been validated at up to |E|=40V/cm without producing leakage in CDM-
M SII Ge detectors, allowing sensitivity to a benchmark WIMP with mass M =
χ
I 8GeV/c2andσ=1.8×10−42cm2(withsignificantsensitivityforMχ>2GeV/c2)
. assuming flat electronic recoil backgrounds near threshold. Furthermore, for the
h
p first time we show that differences in Luke-Neganov gain for nuclear and elec-
- tronic recoils can be used to discriminate statistically between low-energy back-
o
ground and a hypothetical WIMP signal by operating at two distinct voltage bi-
r
t ases. Specifically, 99% of events have p-value < 10−8 for a simulated 20kg-
s
a day experiment with a benchmark WIMP signal with Mχ =8GeV/c2 and σ =
[ 3.3×10−41cm2.

PACSnumbers:95.35.+d,07.57.Kp,95.55.Rg,07.85.Fv,29.40.-n
1
v
5
8
1 Motivation
6
3
. Forlow-massWIMPs(Mχ <10GeV/c2),theenergytransferinanelasticWIMP-
1
nucleon interaction is barely above detection threshold for dark matter experi-
0
ments. In particular, at these recoil energies experiments may lose the ability to
2
distinguish between electron recoils and nuclear recoils, have trouble defining a
1
:
v
1:DepartmentofPhysics,StanfordUniversity,Stanford,Ca94110,USA
i 2:FermiNationalAcceleratorLaboratory,Batavia,IL60510,USA
X
3:DepartmentofPhysics,UniversityofIllinoisatUrbana-Champaign,Urbana,IL61801,USA
r 4:DepartmentofPhysics,SyracuseUniversity,Syracuse,NY13244,USA
a
E-mail:[email protected]
2
fiducial volume, and have poor trigger efficiencies. For these reasons, the limits
at low masses are many orders of magnitude larger than the limits for a heavier
WIMP(M ∼100GeV/c2).
χ
The CoGeNT1 and DAMA2 experiments have unexplained low-energy sig-
nals/modulationthatarecloseenoughtotheCDMS3 andXENON104 limitsthat
some members of the dark matter physics community believe a misestimation
ofsystematicscouldexplaintheexperimentalinconsistencies.Thenewinterdig-
itated CDMS detectors5 should improve our sensitivity to low-mass WIMPs by
an orderof magnitudedue toimproved definitionof thephonon fiducialvolume
atlowenergies,butevenfurtherimprovementshouldbepossiblebymagnifying
theirphononsignalforverylow-energyevents,anideafirstdiscussedandstudied
byPaulLuke6.
2 Luke-NeganovPhononGain
InaCDMSdetector,thee−/h+pairsproducedinaninteractionaredriftedacross
thecrystaltocharge-amplifier-instrumentedelectrodes.Whiledrifting,thecarriers
shed Luke-Neganov phonons equal in energy to the external electronic potential
energyacrossthedetector.Thus,thetotalphononenergy,P,createdinaninter-
t
actionandmeasuredwithTESarraysisasumofthephononsproduceddirectly
intherecoilitself(P)andtheLukephonons
r
P =P +n eV (1)
t r e/h b
wheren isthenumberofe−/h+pairsproducedandV istheexternalbias.n
e/h b e/h
isafunctionofbothP andinteractiontype(nuclear/electronic)andtraditionally
r
iswrittenintermsoftheaverageenergyneededtoproduceane−/h+ pairforan
electronic recoil , ε , and a normalized yield factor, Y, which by definition is
e/h
1 for electronic recoils and for nuclear recoils has been found to roughly follow
Lindhard8 theoryinGe:
n =Y(P,type)P/ε (2)
e/h r r eh
or
P =(1+Y(P,type)V /ε )P. (3)
t r b eh r
In standard operating mode CDMS measures both P and n , and can thus
t e/h
estimateY for each particle interaction individually, allowing discrimination be-
tween electron and nuclear recoils. To maximize this discrimination, we usually
operate at smallV to minimize correlation between P and n . Paul Luke pro-
b t e/h
posed that if instead we operate at large V , then the Luke phonon signal will
b
completelydominatetheintrinsicrecoilsignalandP willsimplybeacalorimet-
t
ricmeasureofn withgainproportionaltoV .
eh b
Unfortunately, there are two experimental constraints which limit the useful-
nessofLuke-Neganovgain.First,fieldandsensorgeometriesmustbechosento
limitinteractionbetweenfreecarriersandcrystalsurfaces7.Second,atveryhigh
voltages(forCDMSII|E|>∼40V/cm)ambientcurrentleakagedominatessen-
sorjohnson/TFNnoiseandthusforour1”Gedevices,V =75Vseemstobenear
b
optimum. At thisV , the Luke-Neganov gain, P/P, for electron recoils is ∼26
b t r
3
asshowninFig.1.Consequently,thethresholdatwhichweexpectgoodfiducial-
volumedefinitionintheinterdigitatedCDMSdetectors,P >750eV,corresponds
t
to electron recoil energy E >30eV . Of course, when operating in this mode
R ee
event-by-eventelectron/neutronrecoildiscriminationisimpossible.
Simulated Wimp Search Spectrum (Pt)
Luke Gain as a function of Bias and Particle Type
30 kgd]101
V/t
e
k
Pt/Pr20 077V55VV N NERRR & ER rch Rate [/100
a
10 P Se10−1
M
WI
00 2 4 6 8 10 100 101
P (keV) Total Phonon Energy, Pt [keV]
r r t
Fig.1 (Coloronline)left:Luke-NeganovGainforvariousV andrecoiltype.right:totalphonon
b
rateestimatesfor2hypotheticalsignals.At0Vbias(solidcurves),anexponentiallyincreasing
lowenergyplusconstantelectronicbackground(red)behavesidenticallytothesum(black)of
aWIMPsignal(green)andaflatelectronicbackground(blue).At75V,thesesametwocases
(samecolorsbutdashed)areeasilydistinguishable.Allcasesincludecontributionsfromnoise-
inducedtriggers(cyan).
DuetothedependenceonyieldoftheLuke-Neganovgain,fornuclearrecoils
thisgainfactorissuppressedby∼×5inthelimitoflargeV .Unfortunately,this
b
means that the fiducial volume threshold recoil energy corresponds to a nuclear-
recoilenergyE >150eV ,resultinginsignificantdegradationofsensitivityfor
R ne
WIMPmassM <2GeV/c2.
χ
On the bright side, this variation in Luke gain with particle type means that
an electron recoil background is preferentially pushed to higher energies, ener-
gies which are not sensitive to a low mass WIMP signal. This effect is clearly
seen in Fig. 1 where the black lines correspond to a benchmark total recoil rate
spectrum on a detector for a M =8GeV/c2 and σ =5.0×10−42cm2 WIMP
χ SI
(green)plusflatelectron-recoilbackgroundof2keV−1kg−1day−1(blue)whichis
r
approximatelytheexperimentallymeasuredlow-energyelectronicbackgroundof
theCDMSIIexperiment9.AtV =0V(solidlines),thebenchmarkWIMPinter-
b
actionrateisdominatedatallenergiesbybackground.Bycontrast,atV =75V,
b
the flat electron recoil background is relatively suppressed to the point that for
P <4keV theWIMPsignaldominates.
t t
Thisnaturalelectronicbackgroundsuppressionmeansthatthesensitivityofa
V =75V Ge WIMP search experiment without background subtraction will be
b
σ ∼1.8×10−42cm2 forM =8GeV/c2,∼50×lowerthantheCoGeNTsignal
SI χ
region,assumingnoexponentialincreaseintheelectronrecoilbackgroundat
lowenergy.
4
Best Fit to Low Voltage WIMP Rate
d) 102
g
k
V/pt
e
k
vt/
e
e (
at 101
R
h
c
r
a
e
S
P
M
I
W 100
0 2 4 6 8 10
Pt (keV)
Fig.2 (Coloronline)FitofsimulatedWIMP+backgroundspectrum(black)tothesum(red)of
anexponentialNRspectrum(green),avariabletriggerthreshold(cyan),andanexponentially
decaying+constantelectronicbackground(blue).
3 NuclearRecoil/ElectronRecoilStatisticalSubtraction
Therecoil-dependentvariationingainresponsealsoleadsinFig.1tovisibleshifts
inspectrumshape.At75V,thebenchmarkWIMP+backgroundmodel(black)has
asignificantexcessofeventsatlowenergiesandasuppressionofeventsathigh
energies relative to the exponential electronic background spectrum (red) which
was chosen to precisely mimic 0V response. This behavior is general; one can
discriminatebetweenelectronicandnuclearrecoilspectrabymeasuringto-
tal phonon distributions at multiple voltages. This possibility to differentiate
betweenelectronicbackgroundandlow-massWIMPsignalsisapowerfulfeature
not shared by CoGeNT, DAMA, or S2-only XENON10 results and adds signifi-
cantdiscoverypotentialtoaCDMSexperimentinthisWIMPmassrange.
To quantify our discrimination capability, we simulate 1000 experiments de-
tectingthepreviouslymentionedbenchmarkratefor400kg-days,andalsosimu-
lateforamuchlargerWIMPrate,σ =3.3×10−41cm2 for20kg-days(bench-
SI
mark2).Tocontrastwiththesesignalsimulations,wealsosimulate1000experi-
mentswithanelectronicexponentialbackgroundthatisidenticallydistributedfor
V =0Vtomaximallyprobeelectronic/nuclearstatisticaldiscrimination.Wethen
b
fiteachofthesesimulatedratemeasurementstoasumincludingarandomnoise
contributionoftheformNe−Pt/εe,acontributionfromelectronrecoilswhosere-
coil energy is distributed according to form Ce+Ree−ER/εr, and, if WIMPs are
included in the fit, a contribution from nuclear recoils with E distributed ac-
R
cordingtoRne−ER/εn.TherandomnoiseisindependentofVb,theelectron-recoil
backgroundspectrumisespeciallysensitivetoV ,andthenuclear-recoilspectrum
b
isintermediateinsensitivitytoV .Allcontributionsareconstrainedtobepositive.
b
Fits without a nuclear-recoil contribution have 5 degrees of freedom (DOF); fits
with a nuclear-recoil contribution have 7 DOF. A fit of simulated data under the
signalhypothesisisshowninFig.2.
Forthebackground-onlysimulatedexperiments(cyanandmagentainFig.3),
the fit quality for the 2 fits are statistically identical since the log of the likeli-
5
hoodratiodistributionaresmallerthanaχ2distributionwith2DOF(thephysical
constraintsofpositiveratesmeansthattheadditionalsignalDOFarenotalways
optimallyused).
Likelihood Ratio for Fits 100 Simulation P Distributions
Null 20kgd Null 20kgd
WIMP σ=3.3x10−41cm2 20kgd WIMP σ=3.3x10−41cm2 20kgd
F10−1 NWχ2u(I2lMl D4P0O 0σFk=)g5d.0x10−42cm2 400kgd g(P)10−1 NWuIlMl 4P0 0σk=g5d.0x10−42cm2 400kgd
PD Flo
10−2 PD10−2
10−30 20 40 60 80 100 120 10−3 10−15 10−10 10−5 100
2log(L /L )
WIMP+BKGND Bkgnd P value
Fig.3 (Coloronline)left:Loglikelihoodratioforthesignal+backgroundfitversusbackground
onlyfit forthe2 WIMP modelbenchmarks(blue/cyan) andforthebackground onlymodels
(cyan/magenta).right:Statisticalseparabilityassumingaχ2 distributionwith2DOFbetween
nullsimulations(cyan/magenta)andsimulationswithWIMPsignals(green/blue).
Bycontrast,bothsignalsimulations(blue/green)showsizeablefitqualitydif-
ferences,somuchsothattothelevelofstatisticssimulated(>99.8%),thereisno
overlapwiththenullsimulations.Wecanfurtherquantifytheelectronrecoil/nu-
clearrecoildiscriminationpotentialbylookingatconservativep-valuesassuming
a χ2 with 2 DOF null distribution (fig. 3). For the benchmarks, 99% of simu-
latedexperimentshavep-values<10−8 and<2.4x10−6 respectively,indicating
very strong discrimination capability. Best fit WIMP cross sections were found
to be slightly systematically suppressed at 5x10−42±8x10−43cm2(90%CL) and
3.3x10−41±3x10−42cm2(90%CL)forthetwobenchmarks.
4 PotentialSystematics
With such large statistical discrimination capability, systematics will almost cer-
tainlydominateourfinalWIMPsensitivity.Inorderofimportance,thedominant
expectedsystematicsinclude
– Fiducialvolumeleakage:high-radiuselectronicrecoilscanhavecarriertrap-
pingontheoutercylindricalsurfacethatsuppressestheLukephonongainand
thus mimics a WIMP signal. Our standard collection and analysis of ∼106
133Bacalibrationeventsshouldbesufficienttoallowestimationofthiseffect
andcorrectionforit.
– Fiducial volume variation with energy and voltage: misestimates of fiducial
volumethatartificiallymimicratedistributionchangesseeninfig.1canpro-
duceafalseWIMPsignalbutshouldbepreventablewith252Cfcalibration.
– Sensitivity to experimentally unverified Yield at ultra-low energies: through
useofboth133Baand252Cf(whichintheCDMSIIdetectorproducesanevent
6
ratewhichis90%nuclearrecoils)calibrationsourcesatlowandhighvoltages,
inferenceofultra-low-energynuclear-recoilyieldispossible.
– Fit systematics: thefunctional formfor the parameterized fit also created the
simulated Monte Carlo spectra. If actual backgrounds have different shapes,
they may result in poor fits for both the low- and high-voltage rate distribu-
tions,leadingtosuppressednuclear-recoilsensitivity.
5 Conclusion
WithcurrentCDMStechnologyandcryogenicbackgrounds,phononinstrumented
GedetectorsoperatedathighvoltagehavesensitivitytolowmassWIMPs∼2or-
ders of magnitude below the CoGeNT and DAMA signal regions. Furthermore,
even exponentially increasing low-energy electronic backgrounds can be distin-
guished from a low-mass WIMP signal for cross sections an order of magnitude
smallerthantheCoGeNTandDAMAsignalregionsbyalternatingbetweenhigh-
andlow-voltagebias.
Acknowledgements WewouldliketothankD.MooreandJ.Filippiniforvaluablediscussions.
ThisworkissupportedbytheDepartmentofEnergycontractDE-FG02-04ER41295,andinpart
bytheNationalScienceFoundationGrantNo.PHY-0855525.
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