Light Yield Investigation of Titanium Doped Al2

Light Yield Investigation of Titanium Doped Al

O

Crystals for CRESST Dark Matter Search

Masterarbeit

zur Erlangung des akademischen Grades Master of Science in Physics

(M.Sc.)

dem Fachbereich Physik der Universität Siegen

Vorgelegt von Ali Askin

November 2006

Light Yield Investigation of Titanium Doped Al

O

Crystals for CRESST Dark Matter Search

Masterarbeit

zur Erlangung des akademischen Grades Master of Science in Physics

(M.Sc.)

dem Fachbereich Physik der Universität Siegen

Vorgelegt von Ali Askin Matr. Nr. 676337

November 2006

Wissenschaftliche Leitung :

Prof. Dr. Claus Grupen (Universität Siegen)

Dr. Franz Pröbst (Max-Planck Institut Für Physik, München)

i

Abstract

The main goal of CRESST dark matter search is to detect WIMP dark matter particles via their elastic scattering on the target nuclei. Detectors, which are very suitable for this work are the cryogenic detectors, since they have the advantages of high energy resolution, low energy threshold and total energy measurement ability independent of interaction mechanisms.

In the first phase of CRESST pure Al2O3 crystals, which were equipped with superconducting phase transition thermometers, were employed as absorber and as a phonon detector pure Al2O3 proved itself as an excellent phonon detector in the first phase of the experiment.

Since dark matter events are expected to be very rare, the most important point in these challenging searches is to suppress the limiting background events as much as possible to increase the sensitivity. Since the light output results from electron recoils is much higher than the one results from nuclear recoils, effective background suppression is possible by the measurement of phonon and light signals simultaneously and thus in the second phase of CRESST scintillating CaWO4 is used as absorber.

Scintillating crystals play a crucial role in the rare event searches and key point for these searches is to find a crystal not only with good scintillation but also with good physical and radiopurity properties. Usually scintillators are studied at room temperatures and extrapolation of their light outputs may be very misleading if the complex scintillation mechanism at low temperatures is not completely understood.

In order to find the best candidate, continuous and systematic research is required.

As a consequence of this requirement, the light yield of scintillating Al2O3:Ti at low temperature (at about 15 mK) and scintillation mechanism of this crystal was investigated to understand whether this new target material can fulfill the requirements of CRESST experiment.

ii

Contents

1 Introduction to dark matter ...1

1.1 Motivation to dark matter ... 1

1.2 Dynamical evidences for the existence of the dark matter ... 2

1.2.1 Rotation curves of spiral galaxies... 2

1.2.2 Clusters of galaxies... 3

1.3 Dark matter candidates ... 4

1.3.1 Baryonic dark matter ... 4

1.3.2 Non-baryonic dark matter... 5

1.4 Direct detection of dark matter... 7

1.4.1 Experimental requirements... 8

2 The CRESST experiment ...9

2.1 Background sources ... 9

2.2 Experimental setup... 10

2.2.1 The cryostat ... 10

2.2.2 Passive shielding ... 12

2.3 CRESST phase II... 12

2.3.2 The detector module ... 14

3 CRESST detectors ...17

3.1 Detector Principle ... 17

3.1.1 Basic model of cryogenic detectors... 17

3.1.2 CRESST absorbers ... 18

3.1.3 CRESST thermometers ... 18

3.1.4 Readout... 20

3.1.5 Data acquisition system... 21

3.1.6 Measurement of a transition curve ... 23

3.1.7 Detector stabilization... 24

3.2 Model for signal evolution ... 24

3.2.1 Creation of phonons in the absorber... 24

3.2.2 Transmission at interfaces ... 25

3.2.3 Thermal model of the detector... 28

iii

4 The scintillating Al₂O₃:Ti crystals ...30

4.1 The basic of scintillation ... 30

4.1.1 Absorption of the incident radiation... 30

4.1.2 Relaxation process... 33

4.1.3 Thermalization of the low energy secondaries... 33

4.1.4 Excitation and emission of luminescence centers ... 34

4.2 Characteristics of inorganic scintillators... 35

4.2.1 Light yield ... 35

4.2.2 Afterglow... 35

4.2.3 Optical properties ... 36

4.3 The scintillation process in titanium doped sapphire ... 36

5 Experiment setup and data analysis ...38

5.1 Experimental setup... 38

5.2 Data analysis ... 40

5.2.1 Pulse height evolution ... 40

5.2.2 Calibration procedure ... 42

5.3 Results and conclusion ... 45

Bibliography ...47

Chapter 1

1 Introduction to dark matter

What makes up the mass density of the universe? This question could not be answered until today despite increasing experimental and theoretical effort. Doppler shift of galaxies indicates that they are receding from us at a velocity proportional to their distance. In 1933 Zwicky derived the velocity dispersion of galaxies in the coma cluster and could thus estimate the mass of the galaxies with the help of the virial theorem [Zwi33]. When he converted the luminosity into a corresponding mass, the results showed that the non-luminous (dark) matter content of the galaxy cluster is much more than the luminous matter content.

Now it is an unavoidable reality that the universe is dominated by a non-luminous gravitating mass, but the nature of this mass is still unknown. In this chapter the evidences for the existence of the dark matter will be introduced. After that the main candidates and direct detection of the dark matter will be described.

1.1 Motivation to dark matter

At present time, the idea which describes the evolution of the universe is based on successful hot big bang theory that agrees well both with theoretical and observational foundations. The theoretical framework relies on general relativity and on the idea that the geometry of space-time is determined by the energy content of the universe.

From the measurement of cosmic microwave background (CMB), it has proved that the universe at large scales is homogeneous and isotropic and it satisfies Friedman- Robertson-Walker (FRW) metric [Oli97].

_{( )}

(

) ( )

2 2 2 2 2 2

2 sin

t 1dr d

ds dt a r d

kr θ θ φ

⎡⎢

= − + + +

⎢ ⎥

⎣ − ⎦

⎤⎥ (1.1)

The scale factor ^{a t}

( )

As a consequence of expanding universe, the light spectra of distant galaxies shifted toward the red band. In the context of the FRW metric the expansion of the universe is described by the Hubble rate of expansion,

) (

) ) (

(

.

t a

t t a

H = (1.2)

1

1.1. MOTIVATION TO DARK MATTER 2

Friedman’s equation can be written in terms of Hubble parameter H and the critical density ρc as

^{3 2}

c 8

N

H ρ G

π

⎛ =

⎜⎝ ⎠

⎞⎟ and 1 k_{2 2}

Ω − = H a (1.3) So that k = 0, k = +1, k = -1 corresponds to Ωtot = 1, Ωtot > 1, and Ωtot < 1.

Big bang theory seems to predict very successfully the observed relative abundances of light elements, the isotropic and homogeneous expansion of the universe and the existence of CMB. On the other hand this theory poses the problems concerning the initial conditions. It predicts but does not explain finite baryon density, extraordinary flatness and smoothness of the universe on very large scales and the origin of primordial density perturbation that gave rise to cosmic structures.

Cosmological inflation, which is an exponential expansion period in the early universe where the total energy density of the universe is dominated by vacuum energy [Gru05] offers a solution to the above mentioned problems.

Precise measurements on CMB provide convincing evidence which shows that the universe is very close to flat i.e, Ω parameter very close to unity. Baryonic matter represents only a small fraction about 4% of the mass of the universe, while non- baryonic dark matter represents 23% of the matter in the universe. Therefore there is large room for dark energy (73%) [Gru05], which is needed to close the universe.

Standard model of particle physics can not explain the enigma of dark energy and dark matter. These two mysteries need explanations beyond the standard model of fundamental physics interactions.

1.2 Dynamical evidences for the existence of the dark matter

1.2.1 Rotation curves of spiral galaxies

The structure of spiral galaxies consists of a central bulge and a very thin disk, which is stabilized against collapse by angular momentum conservation. The observations revealed that the surface luminosity of the disk falls of exponentially with radius [Fre70].

I

( )

rd

r M

v_rot = G^N (1.5)

GN is Newton’s gravitational constant, M is the central mass, and a keplerian behaviour is obtained. The Doppler shift of spectral lines has been used to obtain their rotation curves, i.e., orbital velocity of the disk as a function of radius [Raf97]. Observations showed that the orbital velocity rises roughly linearly from the

2 /

−1

∝r v_rot

1.2. DYNAMICAL EVIDENCES FOR THE EXISTENCE OF THE DARK MATTER 3

center outward until a certain value, and then stays constant out to the largest measured radii (see Figure 1.1).

Figure 1.1: Observed rotation curve of the nearby dwarf spiral galaxy M33, superimposed on its optical image [Kha02]. The dashed line shows the estimated contribution to the rotation curve from the luminous stellar disk.

From the surface luminosity observations of spiral galaxies, it is concluded that the nature of the non-keplerian (flat) rotation curve is due to the existence of dark matter in the galaxy.

1.2.2 Clusters of galaxies

The largest gravitationally bound systems in the universe are clusters of galaxies. From the virial theorem which one can apply to a gravitationally bound system in equilibrium.

One gets:

2 E_kin = − E_grav (1.6)

where ²

2 1m v

E_kin = is the average kinetic energy of the bound object of mass m,

and r

mG M

E_grav =− _N is the average gravitational potential energy caused by the other bodies. From the measurement of v² via the Doppler shifts of the spectral lines and an estimate of the geometrical extent of the system, one can find its total mass M. In 1933 Zwicky proved that this virial mass of galaxy clusters is far beyond their luminous matter content and that these systems contain large amounts of dark matter. The other evidence which indicates the existence of the dark matter is the x-ray emission of the galaxy clusters. Galaxy clusters are the most powerful x-ray sources in the sky, the emission extends over the entire cluster and indicates a large amount of gas in the form of a hot plasma where x-rays are produced by electron bremsstrahlung.

1.2. DYNAMICAL EVIDENCES FOR THE EXISTENCE OF DARK MATTER 4

Again, the use of the virial theorem to calculate the mass necessary to bind the gas particles, gives a result which approximately agrees with the virial mass estimate from Doppler shifts.

A most recent evidence for the existence of dark matter is the observation of the giant arc-like structures in galactic clusters due to the gravitational lensing effect (see figure 1.2). This situation also gives a rough agreement with other observations [Sad99].

Figure 1.2: Gravitational lensing observed around the galaxy cluster Abell-2218 by the Hubble Space Telescope [Hub]. Due to the lensing a luminous source in the background is seen as many arclets surrounding the cluster.

1.3 Dark matter candidates

Since the idea of completely unknown matter in the universe is quite drastic, the first question could be the nature of this unknown matter.

Baryonic dark matter candidates, i.e., Brown and white dwarfs, neutron stars, stellar black hole remnants, are in the form of standard astrophysical objects generally called Massive Compact Halo Objects (MACHOs), whereas the nature of the non- baryonic dark matter is still unknown and needs explanations beyond the standard model of fundamental interactions. In the following, the main dark matter candidates will be described.

1.3.1 Baryonic dark matter

Baryonic matter strongly interacts with light even if the baryons are non-luminous themselves they would absorb the light and reemit in the infrared. So that baryonic dark matter should be observed either in its emission or absorption lines [Dol99].

1.3. DARK MATTER CANDIDATES 5

From these facts it can easily be concluded that baryonic dark matter can not take the form of hot gas, otherwise one could observe a large x-ray flux, also it can not take the form of cold gas or dust, as they absorb the light and reemit it in the form of infrared, therefore it is possible to observe it through absorption lines. The next possibility, which can be considered are stellar remnants, however, it seems to be impossible because there is no trace of parent stars from which they could arise.

The baryonic dark matter can be considered in the form of MACHOs which include, brown and white dwarfs, neutron stars, stellar black hole remnants. It is not possible to see these objects directly and they were searched via gravitational lensing methods. Neutron stars and black holes would form in supernovae explosions which can contaminate the galaxy with elements heavier than hydrogen and helium and thus can be spectroscopically observed.

When a small and medium size star burns all its hydrogen stock into helium, it will become a white dwarf with an average mass of 0.5-0.6 solar masses and thus can not reach supernovae phase. White dwarfs are the end states of these stars. These stars are not heavy enough to produce core temperatures required to burn carbon in a nucleosynthesis reaction, on the other hand their density is more than that of the sun and therefore they shine brightly. Since stars tend to eject most of their mass into space before the final collapse, the spectroscopical observation would be possible.

If we consider that some part of the baryonic matter is in the form of dead stars, the other part would be the masses which never succeed to be a star. Brown dwarfs have a mass M 0.008 and therefore the temperature in their center is not enough to start a nuclear reaction and thus they shine very dimly from the residual energy due to gravitational contraction. The stellar mass function raises towards small masses (most of the stars are small) and thus one would expect significant numbers of such objects in the galaxy [Raf97].

1.3.2 Non-baryonic dark matter

The classification of dark matter in terms of the large scale structure formation can be divided into two groups

1. Hot dark matter (HDM). For this form of dark matter the structure formation is only possible at very large scales, which is larger than galactic size lstr

»

is formed at the low scale lstr

«

Another important aspect of dark matter is its dissipation property. If the energy loss of the dark matter is easy then the structure formation could proceed faster. Otherwise the cooling of the dark matter would be less efficient and small structures would not be formed. From this point of view there could be two forms of dark matter, dissipationless and or dissipative [Dol99]. Since most of the dark matter candidates are considered as weakly interacting particles, it can be concluded that they are dissipationless particles.

The best motivated and most favorite non baryonic dark matter candidates are neutrinos, axions and weakly interacting massive particles (WIMPs). In the following these three candidates will be presented.

1.3. DARK MATTER CANDIDATES 6

Neutrinos

The only dark matter candidates, which are known to exist, are neutrinos [Kha02].

Neutrinos have a very small mass, do not interact via either the electromagnetic or the strong nuclear force and so are incredibly difficult to detect. This is what makes them appealing as dark matter. But as a possible candidate their lower mass is a restriction to make an appropriate description of the large scale structure of the universe. To give a cosmologically interesting contribution to the cosmic density (Ω), a relatively narrow range mν ~ 1-50 eV is required. A neutrino heavier than this would overclose the universe unless mν >3 GeV, when it would be non-relativistic at freeze-out with a small enough relic abundance to act as a cold dark matter [Ber00]. At the other mass end, a neutrino lighter than 1 eV gives a small and dynamically not very important contribution to cosmic density.

Axions

Axion is a hypothetical elementary particle and emerged to explain the missing CP violation in strong interactions of quantum chromodynamics [Pec77]. It has properties that makes it a good dark matter candidate. These dark matter axions have extraordinarily feeble couplings to matter and radiation, that they were never in thermal equilibrium in the early universe and would behave today as cold dark matter. The mass of the axions is constrained by laboratory searches and astrophysical arguments.

The properties of the axion are basically set by its mass ma. The smaller the axion mass the more weakly the axion is coupled to protons and electrons. If the axion had a larger mass, then it would have had observable influence on stellar evolution and on the dynamics of the supernova 1987A. If we require that the energy density in axions does not ``overclose'' the universe, it requires a mass for the axion which is less than 0.001 eV. Their weak coupling to electromagnetism makes the detection of the axions possible. The presence of a strong magnetic field could result in the decay of axionic dark matter into two photons.

Weakly interacting massive particles (WIMPs)

Weakly interacting massive particles are the hypothetical particles proposed as one possibility of a solution of the dark matter problem. These particles interact through weak nuclear forces and gravity. Since they do not interact with electromagnetism they cannot be seen directly. Wimps are in the form of lightest supersymmetric particle, plausibly lightest neutralino χ, in a mass range between 1 GeV and 1 TeV. The difference between normal and supersymmetric particles can be defined by a quantum number, the so called R-parity,

^R=

( )

R = +1 means ordinary particle and R = -1 supersymmetric particle. The conservation of R parity suppresses or forbids the decay into lighter particles and therefore a relic population of WIMPs is expected.

1.4. DIRECT DETECTION OF DARK MATTER 7

1.4 Direct detection of dark matter

Heavy dark matter particles can be detected either directly by the observation of nuclear recoils or indirectly by the observation of their annihilation products such as high energy neutrinos, charged leptons or gammas. In the calculation of the WIMP direct detection rate, the local dark matter densityρ₀, velocity distributionν = ν^{2 1/ 2}, the WIMP mass and the cross section on the target nuclei are the crucial parameters. ρ0 and

ν can be inferred from the measurement of rotation curve of our own galaxy. The mean density of particles trapped in the gravitational potential well of the galaxy is expected to be ρ0 ≈ 0.3 GeV.cm^-3 [Jun96]. According to this model the local velocity distribution in the galactic rest frame is Maxwellian

( )

(

) (

)

f ³ = 1/ ₀³π^3/2 exp − ²/ ₀^{2 3} , (1.8)

where v0 is the velocity at the local position. The velocity dispersion can be obtained from the asymptotic flat rotation velocity as ν = 3/ 2ν_∞ [Bin87]. As previously explained the measured rotation curve of our galaxy rises until a value of 220 km.s^-1 [Ker86] and then stays constant therefore v_∞ =v₀ =220±20 km.s^-1 andν =270 25± km.s^-1.

Direct detection of dark matter relies on the interaction of WIMP dark matter particles with the target nucleus, causing it to recoil. Since WIMP particles move at non-relativistic velocities, the deposited energy due to WIMP interaction can be calculated as

( )

(

2

+ −

= v

m m

m E m

N w

N w

r

)

where m_w and v are WIMP mass and velocity, respectively, and θ is the scattering angle in the center of the mass frame. The recoil energy spectrum is given by

( ) ( )

v v E f

m F dE

dR ^vesc

v r

r ⁼ W

∫

min

2 1 2 0 0

2 µ

σ

ρ , _{min 2}

2^rµ ^N m

v = E , (1.10)

where f1(v) is the velocity distribution with respect to the detector, mN is the target nucleus mass, µ = (mw mN)/ (mw + mN) the reduced mass, Er is the recoil energy transferred to the nucleus and F(Er) is the form factor and σ0 is the WIMP-nucleus interaction cross section. The term vmin is the minimum WIMP velocity able to generate a recoil energy Er, and vescis the maximum WIMP velocity set by the escape velocity in the halo model.

The WIMP-nucleus cross section can have both spin independent (scalar) and spin dependent (axial) components. The spin independent interaction is coherent across the nucleons in the nucleus, whereas spin dependent interaction is possible for nucleons with nuclear spin and the spin dependent interaction cross section is proportional to J(J+1) rather than to the number of nucleons as in the case of spin independent cross section. In most cases, the coherent term will dominate because of its A² enhancement [Gai04].

1.4. DIRECT DETECTION OF DARK MATTER 8

1.4.1 Experimental requirements

Despite the rare interaction of WIMP dark matter particles, their detection is still potentially possible. The flux of WIMPs is assumed to be quite large but the problem lies in the interaction with ordinary matter. The challenge for dark matter experiments is to design an experiment that should have an energy threshold as low as possible due to the few KeV energy deposition, it should have large mass (many kilograms) of detector material due to the small cross section of WIMP-nucleus elastic scattering and highly suppressed background in order to allow a spectrum of rare nuclear recoils to be observed.

9

Chapter 2

2 The CRESST experiment

CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) attempts to detect WIMP dark matter particles via the energy transferred to a nucleus due to the elastic scattering of WIMP dark matter particles on the target nuclei.

Since dark matter events are expected to be very rare, such experiments have to be shielded carefully against cosmic radiation and ambient radioactivity. To increase the sensitivity of the CRESST experiment, passive background suppression was achieved by careful selection of materials and by placing the experiment in a deep underground site. In this section the setup of the CRESST experiment in Gran Sasso will be described. The main background sources and the detector module of the second phase of CRESST will be explained.

2.1 Background sources

The sensitivity of the CRESST experiment is limited by the backgrounds induced either by cosmic radiation or residual radiation emitted from the experimental and other materials surrounding the detectors.

Cosmic rays are extremely energetic particles, primarily protons and alpha particles, which originate in the sun, other stars, supernovae and some of the violent cataclisms which occur in the far reaches of space. The cosmic ray particles interact with the upper atmosphere of the earth and produce showers of lower energy particles.

Many of these lower energy particles are absorbed by the earth’s atmosphere as they travel down to the surface. Cosmic radiation at sea level consists of 70 % muons, 30 % electrons and less than 1 % protons and neutrons. Because of their high penetration ability, muons play an effective role in the production of the background directly by depositing energy in traversing the detector itself. This situation results in the creation of primary and then secondary electrons and finally photons. Direct energy deposition in the detector leads to an enormous energy deposition much higher than the energy range of interest, or indirectly by interacting with materials surrounding the detectors results in X-ray, γ-ray, and neutron emission.

Environmental radioactivity is due to the primordial radionuclides, which are left over from when the world and the universe were created. They are typically long lived, with half-lives often on the order of hundreds of millions of years. The most common primordial radionuclides are ⁴⁰ K, a β unstable element with an isotopic abundance of 0.012 % and ⁸⁷Rb, which is a pure electron emitter and has 27.8 % isotopic abundance.

Four natural radioactive decay chains of uranium, thorium and actinium also belong to the primordial radionuclides and they are the dominant environmental background

2.1. BACKGROUND SOURCES 10

source. Their half live are on the order of the age of the universe and their activity is still observable today. The man made radionuclides, the most important ones are ⁹⁰Sr and ¹³⁷Cs both of them are electron emitters and contribute to the background.

2.2 Experimental setup

As previously mentioned, one of the dominant background sources is the cosmic radiation and mainly due to the muons. The suppression of this cosmological radiation is achievable by placing the experiment in a deep underground site.

Figure 2.1: Planimetry of LNGS underground laboratories

Because of that, the CRESST experiment is located at the Laboratori Nazionali del Gran Sasso (LNGS ) in a low background facility (Figure 2.1).

The laboratory is situated in the highway tunnel of the Gran Sasso mountain at an average depth of about 3500 meter water equivalent. This results in a reduction of the cosmic muon flux by 6 orders of magnitude to about 1 m^-2h^-1. Only sea-level cosmic ray muons of more than 1 TeV can reach the underground laboratories [dGS].

The existence of the rock overburden acts as a strong shield against cosmic rays but on the other hand it is itself a source of radioactivity because of the existence of natural radionuclides in the structures of rock.

2.2.1 The cryostat

The central part of CRESST set-up at LNGS is the cryostat. It provides a base temperature of about ~ 5 mK to operate the detectors.

The CRESST cryostat is a ³He / ⁴He dilution refrigerator. Figure 2.2 shows the cross section of the cryostat and the shielding. Because of the sensitivity requirements of the experiment, the cold box, which houses the detectors, is well separated from the rest of the refrigerator. The transfer of the refrigerators’ cooling power to detectors is

2.2. EXPERIMENTAL SETUP 11

realized by a 1.5 m long cold finger made of low background copper. To block the radiation, which could come from the refrigerator into the experimental volume, a 20 cm thick lead shield is placed between mixing chamber and cold finger. This shield and another shield which is thermally anchored to the liquid nitrogen bath surround the cold finger.

Five concentric radiation shields made from low background copper surround the experimental volume and serve as the cold box.

Figure 2.2: Schematic view of the CRESST cryostat and passive shielding.

The experimental volume can carry up to 10 kg of target mass. To decrease the vibrating effect of the boiling nitrogen and helium, detectors are mounted on a spring supported platform. The isolation of the cryostat against mechanical vibrations is

2.2. EXPERIMENTAL SETUP 12

established by hanging the cryostat from a 20 cm thick wood plate which rests on air dampers and the isolation against the electromagnetic interferences is done by placing the cryostat and experimental volume in a Faraday cage.

Since clean conditions are very important during the mounting of the detectors the ground floor of the Faraday cage is equipped as a class 100 clean room.

2.2.2 Passive shielding

In order to shield the environmental radiation, it is required to use high Z materials such as lead and radiopure materials like copper. Lead is a strong photoelectric absorber therefore it is generally used for γ shielding. Also the probability of radioisotope production via cosmological interactions is very low for lead.

Together with the low background copper, the above explained properties of lead makes the use of these materials mandatory as the passive background shield of the CRESST experiment.

The external shield of the cold box consists of two closely fitting halves of 14 cm of radiopure copper (directly surrounding the cold box) and followed by 20 cm thick lead (²¹⁰Pb activity of 35 Bq.kg^-1 [Büh96]). The entire shield is enclosed in a gas tight radon box that is flushed with nitrogen gas and maintained at a slight overpressure in order to prevent radon from penetrating the shielding.

The entire shielding is on rails so that it can be opened without handling the individual pieces.

Another important point in WIMP searches is the neutron background. Neutrons can scatter on the target nuclei and imitate the rare expected WIMP signals. Thus a 50 cm layer of polyethylene is employed as a neutron moderator and placed outside the radon box.

Finally, the installation of a muon veto system around shielding helps to block neutrons, which are induced by interaction of muons with the lead shielding.

2.3 CRESST phase II

In the first phase of CRESST pure sapphire crystals (Al2O3) were employed as absorber to detect the WIMP dark matter particles via their elastic scattering on the absorber nuclei. Sapphire crystals were equipped with a tungsten superconducting phase transition thermometer evaporated onto one surface of the crystal. The evaporation process of tungsten takes place at high temperature (~ 500 ^oC). The high melting point of the sapphire prevents the inter-diffusion between the tungsten film and the crystal, and a transition temperature of the tungsten thermometer at about ~ 15 mK can be obtained without the need of any barrier placed between crystal and film. Sapphire has the advantage of having a high Debye temperature (ΘD = 1040.8 K), this means a high speed of sound [Ash76], which facilitates the fabrication of a sensitive detector with low energy threshold. Sapphire is a highly radio-pure material and the existence of Al with ground state nuclear spin 5/2 makes this absorber fully sensitive to spin-dependent WIMP–nucleon interactions. But as a phonon detector pure sapphire measures the total energy deposited by a particle interaction in the absorber, independent of the interaction mechanism. In the first phase of CRESST, it was seen that sapphire is an excellent cryogenic phonon detector with low energy threshold.

2.3. CRESST PHASE II 13

The main aim in the second phase of the CRESST is to increase the sensitivity for WIMP detection by active background suppression with simultaneous detection of phonon and light signals. In CRESST II scintillating calcium tungstate (CaWO4) is employed as absorber. In contrast to WIMP-nucleon interaction, the background events from radioactive contamination of the crystals and surrounding materials and cosmic radiation deposits energy mostly by electron recoils, which are characterized by a higher ionization and scintillation efficiency. Thus the use of a cryogenic phonon detector in conjunction with a light detector makes an event by event discrimination possible.

The reasons for using calcium tungstate in the second phase of CRESST are its high atomic mass (because of the presence of tungsten as heavy nucleus), this increases the spin independent interaction cross section, which is proportional to A², its high light output at low temperature and the absence of a noticeable degradation of the light yield for events near the crystal surface.[Meu99].

Proof of principle

The proof of principle detector was constructed to prove the idea of active background suppression by the simultaneous measurement of the phonon and light signal. The setup consists of two independent detectors. A 6 g CaWO4 scintillating crystal with a tungsten superconducting phase transition thermometer and a second calorimeter placed next to it to detect the scintillation light [Meu99].

Figure 2.3: Results of the proof of principle experiment in terms of the pulse height in the light detector versus pulse height in the phonon detector. The scatter plot on the left side has been measured with an electron and photon source, while a neutron source was added to measure the plot on the right [Meu99].

Figure 2.3 shows the results of the proof of principle experiment in terms of the pulse height in the phonon detector versus pulse height in the light detector. The left hand plot exhibits the result obtained by irradiating the crystal with 122 and 136 keV photons from a ⁵⁷Co source together with electrons from a ⁹⁰Sr β source. The signal in the phonon detector measures the total energy independent of the interaction mechanism.

2.3. CRESST PHASE II 14

The right hand plot was taken by adding an americium beryllium neutron source to the above mentioned photon and electron sources. It proved that the light output due to the electron recoils is much higher than the light output of the nuclear recoils of the same energy. The ratio of the light yield from electron recoils to the light yield of the nuclear recoils gives the quenching factor of the crystal. The ratio for nuclear recoils caused by neutrons was found to be 7.4 and 3.6 for α particles.

2.3.1 Motivation for investigation of alternative targets

.

As already mentioned, in the second phase of CRESST the main aim is the sensitivity enhancement by the use of scintillating crystals. Scintillating crystals could respond positively to the alternative target requirements of the experiments looking for dark matter particles, thanks to plenty of suitable materials, while allowing at the same time a strong particle identification power [Cor04].

In order to suppress the limiting backgrounds (α,β,γ events from radioactive contamination of the crystals and surroundings materials and cosmic radiation ), the key point is to find crystals with good scintillation properties at low temperatures.

Usually scintillators are studied and used at room temperatures and the extrapolation of light outputs to low temperatures may be very misleading as long as the complex scintillation mechanisms at low temperatures are not fully understood. In order to find the best candidate systematic research and development studies at low temperatures are required.

As a phonon detector pure sapphire proved itself in the first phase of the experiment and the main aim of this work was the investigation of the light yield of the titanium doped sapphire (Al2O3:Ti) crystals, which would be a very good candidate for future dark matter searches at low temperatures.

2.3.2 The detector module

The prototype detector module of CRESST II consists of a 300 g cylindrical CaWO4

crystal of 40 mm diameter and height, operated as a cryogenic calorimeter (the phonon channel) and a nearby but separate cryogenic light detector optimized for the detection of the scintillation photons (the light channel) (Figure 2.6). Both channels are supplemented with a tungsten Superconducting Phase transition Thermometer (SPT).

Figure 2.4 shows a schematic view of a prototype module.

The light detector is mounted close to a flat surface of the CaWO4 crystal and the inner surface of the detector holder is covered with a highly reflective polymeric multilayer foil to increase the light collection efficiency.

Phonon channel

The function of the phonon channel is to measure the energy transferred to the nucleus of the CaWO4 crystal in a WIMP-nucleon elastic scattering [Ang05]. Among different scintillating crystals CaWO4 is selected as absorber because of its high light yield at low temperature and the high atomic mass of W makes this crystal a promising material for WIMPs with coherent (spin independent) interaction. Compared to sapphire, which was the target material in the first phase of the experiment, CaWO4 has a few drawbacks. The low Debye temperature of CaWO4 (ΘD = 228.4 K [Glu73])

2.3. CRESST PHASE II 15

Figure 2.4: Schematic view of the prototype detector module

would limit the achievable threshold and it needs a SiO2 layer as a interdiffusion barrier before the evaporation of the tungsten film to obtain a transition temperature of the thermometer of ~ 15 mK [Fra02].

Light channel

The cryogenic light detector used to detect the energy of the scintillation photons consists of a silicon wafer with a tungsten SPT evaporated on it. Only a small fraction of the deposited energy (~1%) in the absorber can be detected as scintillation light. Thus strong efforts have been made to increase the detection efficiency and sensitivity of the light detector

To increase the sensitivity of the light detector it is required to reduce the heat capacity of the thermometer. This is achievable by reducing the area of the thermometer film [Pet05]. To increase the phonon collection efficiency the original tungsten film is equipped on both sides with aluminium phonon collectors. These collectors provide 1mm² collection area (figure 2.5).

2.3. CRESST PHASE II 16

Figure 2.5: Schematic view of the phonon sensors of the light detector used in the CRESST phase II prototyping phase. The sensor is a 40 mm diameter Si on sapphire wafer.

Figure 2.6: Picture of an open detector module for CRESST phase II.

Chapter 3

3 CRESST detectors

Since the kinetic energy of a recoiling nucleus due to WIMP interaction is very low (on the order of a few tens of keV), it is therefore difficult to detect it with conventional detectors. CRESST detectors include a target crystal to absorb the incoming particle, a superconducting phase transition thermometer to measure the temperature rise and therefore the energy resulting from the particle interaction in the absorber and a light detector to detect the scintillation light.

Operation of this combination at low temperature (~ 15 mK) provides the ability for high energy resolution, low energy threshold, total energy measurement independent of the interaction mechanism and active background suppression.

In this chapter the general detection principles of low temperature detectors will be explained with a detailed description of detectors developed for the CRESST experiment.

3.1 Detector Principle

3.1.1 Basic model of cryogenic detectors

A cryogenic detector consists of an absorber, in which a particle interaction takes place and a small temperature sensor evaporated onto one surface of the absorber to measure the temperature rise and therefore the energy deposited by particle interaction. This temperature sensor is weakly thermally linked to the mixing chamber of the cryostat with a thin gold wire.

According to the simplified model of calorimeters, any energy deposition, ∆E, in the absorber due to the particle interaction causes a rise in the temperature of the absorber that can be written as

C T = ∆E

∆

where C is the heat capacity of the absorber. The system relaxes back to the equilibrium temperature via the thermal connection to a heat sink.

Due to the absence of conduction electrons the heat capacity of dielectric materials at low temperature is dominated by the phonon system, for which C ∝ ( T / ΘD )³. The T³ dependence makes the heat capacity of the absorber small enough at low temperatures to obtain a measurable temperature rise from a particle interaction.

17

3.1. DETECTOR PRINCIPLE 18

3.1.2 CRESST absorbers

WIMP dark matter particles are detected by nuclear recoil events, which take place in the absorber crystal. Thus the absorber materials are the key elements in the rare event searches and the properties of the material should fulfill the requirements of the experiment.

In the first phase of the CRESST experiment sapphire was used as the absorber.

Sapphire is a dielectric material and therefore has a small heat capacity at low temperatures. High Debye temperature of this material means high speed of sounds for phonons which results in a sensitive detector with low energy threshold. Since the sensitivity of the experiment is mainly limited by residual radioactivity, the most important requirement for the rare events searches is the radiopurity of the material being used as absorber. At this point sapphire completely satisfies this requirement. It contains only stable isotopes of ¹⁶O (99.76 % isotopic abundance ), ¹⁷O (0.04 %), ¹⁸O (0.2 %) for the oxygen and 100 % ²⁷Al [Coz 03].

The idea, to separate background events from the nuclear recoils to increase the sensitivity, created the need of using a scintillating crystal. In the second phase of CRESST, scintillating CaWO4 crystals were employed as the absorber.

3.1.3 CRESST thermometers

The temperature rise due to a particle interaction in the absorber is read out by a tungsten superconducting phase transition thermometer. This sensor consists of a tungsten thin film evaporated onto one surface of the absorber with a typical thickness of 1-2 kA^o. The detectors are operated within the superconducting to normal transition of the thermometer, where a very small temperature rise, ∆T, of the thermometer leads to a relatively large increase of its resistance, ∆R.

The ∆T induced by a particle in the energy range of interest is much smaller than the width of the transition, so that there is an approximately linear relation between ∆T and ∆R. Figure 2.6 shows a measured transition curve of a tungsten thermometer. The performance of each detector is defined by the heat capacity of the thermometer and the two parameters of the transition curve: The dynamical range of the SPT is defined by the width of the transition curve. The sensitivity of the thermometer depends on the slope of the transition curve.

Stabilization of the detectors during the operation is of crucial importance. So that an additional heater structure is used to stabilize the detector at the desired operating point within a few µK. Each thermometer is equipped with a thin gold pad structured in the middle of the thermometer. Figure 2.7 shows the structure and electrical connection of the thermometer of the phonon channel. The electrical connection of the heater, which is the 25 µm gold wire connected to the gold pad in the phonon detector, is done onto two aluminium pads placed close but separate on both sides of the gold pad. The connection from these two aluminium pads to the isolated contact pads of the holder is established via thin aluminium wires and the electrical connection from the contact pads to the heater circuit is realized with twisted pairs of superconducting wires. For the thermal coupling and ground connection of the thermometer, a direct connection is made with a 25 µm Au wire from the Au pad to the detector holder, and through a copper wire the detector holder is connected to the mixing chamber of the cryostat. This copper wire acts as a low pass filter and reduces the influence of fast temperature

3.1. DETECTOR PRINCIPLE 19

fluctuations of the mixing chamber.

Figure 3.1: Measured transition curve of the tungsten film. A very small temperature rise results in a measurable increase in resistance.

The same heater is used to send both control and heater pulses to keep the detector at the desired operating point and to monitor the detector stability, respectively.

Figure 3.2: Structure and electrical connection scheme of the thermometer used in the phonon channel.

3.1. DETECTOR PRINCIPLE 20

3.1.4 Readout

The working principle of the readout system relies on the reading of the resistance change with temperature. As shown in figure 2.8, the thermometer is connected in parallel with a 50 mΩ reference (shunt) resistor, which is connected in series with the pick up coil of a Superconducting QUantum Interference Device ( SQUID ). A constant current, I0, is sent to the circuit and shared between the two parallel branches. The current of the SQUID branch, Is, can be calculated from the equation

( ) ( )

f f

s R T R

T I R

I = ₀ +

.

A SQUID is the most sensitive magnetic flux detector. It consists of a superconducting ring with two Josephson junctions. When the SQUID is biased with a current greater than the critical current, the voltage across the SQUID is modulated with the flux penetrating the SQUID loop with a period of one flux quantum φ₀ =h/2e [Hon03]. Thus the SQUID is a flux to voltage transducer with a periodic transfer function.

A separate feedback coil is used to keep the flux through the loop constant, the SQUID is operated in a flux locked mode. By this way a linearity is obtained between the induced magnetic flux due to the increasing branch current, Is, and the output voltage

(

) ,

φ0 represents the magnetic flux quantum.

Figure 3.3: Readout circuit for the thermometer

3.1. DETECTOR PRINCIPLE 21

The speed of this read out system is limited by the compensation of the maximum flux change penetrating SQUIDs’ input loop by the feedback coil of the SQUID, namely the slew rate. Short term temperature control can be maintained by using the base line of the SQUID output voltage between pulses as the temperature indicator and then regulating the current to the heater on the thermometer. This system deals with flux quantum losses in the SQUID by not responding to large (φ₀/2) jumps in the SQUID base line if they occur very quickly. This situation was taken into account and a second independent control loop was implemented to provide long term stability.

SQUIDs used for CRESST are commercial DC SQUIDs. They are mounted in the helium bath of the cryostat. The shunt resistors are thermally coupled to the mixing chamber to reduce their Johnson noise. A floating current source provides a constant current for the read out system, and electrical connections from the detectors to SQUID are realized with twisted pairs of superconducting wires.

3.1.5 Data acquisition system

Figure 2.9 shows a schematic representation of data acquisition system used in the Munich and Gran Sasso facility.

For the detector operation, the required low temperature is provided by the cryostat and detectors are mounted via their holder to the base plate of the cryostat. The detector holders are electrically and thermally insulated from the base plate and thermal connection is made by a thin copper wire from the detector holder to the mixing chamber in order to provide a thermal relaxation time of a few hundred seconds. The thermal connection between the holder and the thermometer is realized with a 25 µm Au bond wire, this wire also acts as the ground connection of the readout circuit. The temperature of the mixing chamber is measured by a carbon resistor (speer), and a heating resistor is used to regulate it. An AC resistance bridge is used to readout the speer and a Proportional Integral Differential (PID) controller regulates the power input into the heating resistor of the mixing chamber. The electrical connections of thermometer is established from the two aluminium pads placed on both ends of the thermometer to the isolated contact pads by superconducting aluminium wires. The connection of thermometer to the read out circuit is established with twisted pairs of superconducting wires, which are screwed to the contact pads to avoid the radioactivity of soldering material. A voltage controlled floating current source provides a constant current for the read out circuit.

The SQUID sensors are placed in the liquid helium bath at 4.2 K. The SQUID output signal passes through a differential amplifier and leaves the Faraday cage through a 50 kHz low-pass filter and is fanned to the trigger generator to produce a trigger signal which triggers the digitizer, while the signal itself passes through an antialiasing low pass filter and is DC- coupled to a 16 bit digitizer. The post trigger sampling cycle of the digitizer is activated by the trigger signal.

Two 25 µm thin Al wires connect gold pad (heater for light detector) constructed in the middle of the light detector’s thermometer to the isolated contact pads placed on the detector holder. The thermometer of the light detector is connected to these contact pads via Al wires through Al phonon collectors structured on both ends of the thermometer.

The heater is then connected to a heater circuit consisting of a summing amplifier and followed by an analog square rooter. Since the same heater is used to inject periodic heater pulses and control pulses, and since there is a quadratic

3.1. DETECTOR PRINCIPLE 22

dependence between the heating power and applied current, it is required to use the square rooter to linearise the relation. The heating power, and thus the stability of detectors is controlled by a computer controlled Digital to Analog Converter (DAC) connected to the summing amplifier. A pulse generator is used to create heater pulses resembling the particle pulses. To produce pulses with different amplitude to cover the whole dynamic range of the thermometer, the single amplitude pulse from the pulse generator is fed into a multiplier module controlled by an external voltage produced by a DAC. To adjust the heater signals according to the dynamical range of each detector the output signal of the multiplier is fed into an attenuator.

Figure 3.4: Block diagram of the data acquisition systems. The temperature levels of the cryostat are represented by horizontal divisions.

3.1. DETECTOR PRINCIPLE 23

3.1.6 Measurement of a transition curve

The performance of each detector depends on the shape of the transition of the SPT from normal conducting to the superconducting region. The current used to bias the thermometer, I0, has a strong influence on the shape of the transition and the transition curve measurement of each film is done with different bias currents in order to optimize the detector response. Usually higher currents mean steeper and often more linear transition, on the other hand the self heating and critical current effects limit the maximum level of current that can be applied to the thermometer. Figure 2.10 shows a measured transition curve of a thermometer with different bias currents.

Usually the performance of each detector is defined by two parameters. The sensitivity of the detector depends on the slope of the transition curve when the SQUID output is plotted versus temperature, and the dynamical range of the detector is defined by the width of transition. The choice of the operating point is mainly a compromise between sensitivity and the linearity of the response.

Figure 3.5: A measured transition curve of a SPT with different bias currents.

During the measurement, the bias current is switched from +I0 to –I0 in order not to depend on the flux quantum state of the SQUID and half of the output step of the SQUID is taken as the transition curve. The temperature can be swept up and down around the critical temperature either by keeping the base temperature (TB) of the cryostat fixed and changing the temperature of the film by changing the current sent into the heater or by sending zero heating current to the film heater and varying the base temperature via the mixing chamber heating resistor. Usually, stabilization at the selected operating point is done with the heater of the thermometer, therefore the first method is chosen for the stabilization.