Physik-Department Light Yield Measurements of Cadmium Tungstate and Titanium Doped Sapphires for the CRESST Dark Matter Search

(1)

Physik-Department

Light Yield Measurements of Cadmium Tungstate and Titanium Doped Sapphires for

the CRESST Dark Matter Search

Diploma Thesis by Raphael Kleindienst

2nd of December, 2010

(2)

(3)

Abstract

Astrophysical observations reveal large amounts of Dark Matter in the universe, of which the largest fraction cannot be baryonic. The nature of this Dark Matter is unknown, a popular class of candidate particles are called WIMPs (Weakly Interacting Massive Particles), which arise naturally from supersymmetric extensions of the Standard Model of particle physics.

The CRESST (Cryogenic Rare Event Search using Superconducting Ther- mometers) Dark Matter search aims at directly detecing WIMPs as they scatter off nuclei in an earthbound target. This is done by cooling scintilling CaWO4 crystals down to milikelvin temperatures and measuring the temperature increase caused by particle interactions. A coincident measurement of the emitted scintillation light allows an active discrimination of common radioactive background. Furthermore, the background rate is suppressed by various layers of passive shielding, a muon veto and by the experiment being located in the LNGS underground laboratory.

Only∼1% of the energy deposited in a CaWO₄ crystal is converted into detected scintillation light. A greater light signal would improve the background separation and lower the energy threshold of the experiment. This is of great effect, as the count rate of WIMP interactions is expected to increase exponentially towards low energies. A straightforward way of accomplishing this, is by using a target with a comparatively higher light yield.

Within this work, CdWO4 and titanium doped Al2O3 crystals were investigated concerning their suitability as a CRESST target. The high density of heavy nuclei in CdWO₄ , as well as the suspected high light yield, makes it an interesting candidate. However the problem of the intrinsic radioactivity has to be addressed and the high light yield confirmed. With only light nuclei, Al₂O₃:Ti crystals of different Ti³⁺ dopant concentrations were investigated specifically in the context of a low mass WIMP scenario. The main focus of the work is on the light yield measurements performed at milikelvin temperatures.

(4)

(5)

An Introduction to Dark Matter

The concept of Dark Matter first appeared in the appendix of a paper discussing redshifts of extragalactic nebulae in 1933 [1]. Today, Dark Matter is firmly estab- lished in modern cosmology and at the focus of many astrophysicists’ attention.

This is because even though the case for Dark Matter is strong, its nature has so far remained elusive. In this chapter, various indirect evidences will be reviewed.

Afterwards, possible Dark Matter candidates are introduced and discussed.

1.1 Evidences for Dark Matter

During the last decades, various indirect evidences for Dark Matter have been brought forth - based on observations at scales ranging from galactic to cosmological.

1.1.1 Rotation Curves

On the galactic scale, evidence of Dark Matter can be found by looking at the orbital velocity of stars as a function of their distance from the galactic center. From simple Newtonian mechanics the orbital velocityv(r) is:

v(r) =

rGM(r)

r (1.1)

where M(r) denotes the mass within the respective orbit. If one looks to the center of a galaxy and assumes a constant density distribution, one hasM(r)∼r³ which implies v(r) ∼ r. At very large radii beyond the luminous disc, all visible matter is enclosed in the orbit and thus M(r) = const. For these large radii one expects to find v(r) ∼ r^−1/2 and thus a vanishing rotational velocity for r → ∞.

With these predictions at hand, the rotation curves were measured to distances far beyond the luminous disk. This was done by measureing doppler shifts of the 21 cm line of neutral hydrogen. As seen from figure 1.1, the orbital velocities stay almost constant at high radii, indicating a hidden mass density distribution scaling with approximatelyρ(r)∼r⁻². A more detailed description of galactic dark matter halos can be found in [2].

(8)

Figure 1.1: Rotation curve of the M33 galaxy as measured by [3]. Data points as well as best fit are shown in white. Also shown are the individual contributions of the galactic disk (yellow), gas (red) and dark matter halo (blue). Image taken from [4].

1.1.2 Kinematics of Galaxies in Clusters

The virial theorem gives an equation relating kinetic and potential energies for stable, bound systems. For systems bound by a gravitational potentialV, the equation looks like:

hTi=−1

2hVi (1.2)

where the brackets indicate an average over time. In 1933, Fritz Zwicky analyzed the velocities of galaxies in the Coma Cluster using the virial theorem [1]. Observational data indicated that the galaxies moved with velocities higher than could be bound by the visible matter. From this, Zwicky inferred a hidden gravitational potential, caused by what he named ’Dark Matter’.

1.1.3 CMB Anisotropies

The precise measurements of the anisotropy of the cosmic microwave background (CMB) radiation offer quantitative evidence of Dark Matter at cosmological scales.

In the early stages of the universe, stable atoms could not form permanently, as photons rapidly dissociated any hydrogen being formed in the galactic plasma.

The universe remained ionized until it had expanded sufficiently and cooled down to a temperature of around 0.3 eV. As stable hydrogen formed (the event being labeled recombination), the density of free electrons decreased so far as to allow photons to propagate freely without scattering through the universe. These photons are referred to as the CMB today. Their energy distribution closely follows a black body spectrum of temperature 2.725 K.

(9)

Figure 1.2: Core region of the Coma Cluster. Photograph taken by the Misti Moun- tain Observatory.

The CMB gives us a snapshot of the matter density distribution at the time of recombination. A lot of effort has been put into examining the CMB. It has been found to be highly isotropic, with relative fluctuations in the magnitude of only 10⁻⁵ at the angular scale of several degrees, taking into account the relative movement of the Earth against the CMB.

The precise measurements of the CMB and its anisotropies give stringent limits on the individual contributions to the energy density of the universe [5]:

• Baryonic Matter ΩB= 0.0449±0.0028

• Dark Matter ΩDM = 0.222±0.026

• Dark Energy ΩΛ= 0.734±0.029

Here, the Ω_i give the energy density contributions as a fraction of the critical density. Summing the individual contributions, one arrives at:

Ω_tot =X

i

Ω_i = 1,003±0,01 (1.3)

which is compatible with a flat universe.

1.2 Dark Matter Candidates

It is apparent, that ordinary luminous matter cannot explain several astrophysical observations. Furthermore, from analysis of the CMB and of Big Bang Nucleosyn-

(10)

thesis, strong limits are set on the total energy density contribution of baryons in general. Before looking at possible Dark Matter candidates in- and outside of the Standard Model, some of the properties such a candidate must fulfill are considered:

• As we have not observed Dark Matter directly, it follows that it hardly interacts with ordinary matter. Therefore it must be electrically and colour neutral, as not to emit or absorb electromagnetic radiation as well as partake in strong interactions.

• Dark Matter candidates may interact weakly, which would open up a possibility for detection.

• Simulations of the structure formation in the universe show that Dark Matter had to be non-relativistic in the early universe. In this context it is referred to asCold Dark Matter.

• Evidences for Dark Matter show up in the study of the early universe (structure formation/CMB), as well as in recent observations (rotation curves, kinematics in galaxy clusters). This suggests stable Dark Matter particles, at least on the time scale of the age of the universe.

1.2.1 Neutrinos

At first glance, neutrinos are very attractive Dark Matter candidates. They are electrically and colour neutral. Furthermore the discovery of neutrino flavor oscillations show they have a non-zero mass. However, as neutrinos are relativistic, they would constitute to Hot Dark Matter and thus cannot give dominant a contribution. Ad- ditionally, constraints on neutrino mass and number density [6] give an estimation of their total energy density of:

0.005<Ω_{N eutrino} <0.015 (1.4) 1.2.2 WIMPs

The acronym WIMP stands for Weakly Interacting Massive Particle. The term includes any particle from outside the Standard Model, which interacts weakly and gravitationally only. WIMP candidates arise naturally in supersymmetric theories.

The core principle of these theories is that all particles of the Standard Model have a supersymmetric partner which differs by spin 1/2. Thus the supersymmetric part- ners of bosons are fermions and vice-versa. As no superpartners have been detected up to this point, the supersymmetry is assumed to be broken.

In the Minimal Supersymmetric Standard Model (MSSM), the quantum number R is introduced, defined as:

R:= (−1)^3B+L+2s (1.5)

(11)

where B,L and s denote baryon, lepton and spin number. Particles of the Stan- dard Model thus haveR= 1 whereas their superpartners haveR=−1. Within the MSSM, it is assumed that the quantum number R is conserved. This means that the Lightest Supersymmetric Particle (LSP) in this model can only be destroyed via pair annihilation and is thus stable. This makes it a very interesting Dark Matter candidate, especially as it arises naturally from extensions of the Standard Model.

Depending on the exact model, different particles take on the role of the LSP. As a hypothetical Dark Matter particle, the lightest of the four neutralinos (commonly denoted asχ) is currently favored. Neutralinos are mixture states of the Bino, Wino and Higgsino; these are the superpartners of the B and W gauge bosons and the currently still undiscovered Higgs boson.

Within theoretical models, estimations of expected neutralino masses are possible. This stems from the requirement, that viable Dark Matter candidates must produce correct relic densities. A Dark Matter candidate produced in the early universe starts off in equilibrium i.e. χχ¯ p¯p where p denotes any Standard Model particle. The annihilation reaction happens at a rate:

ΓA=hσ_Avi ·nχ (1.6)

where σ_A is the annihilation cross section, v the relative velocity, n_χ the number density and the brackets denote a thermal average. As the universe expands, particles encounter each other less frequently and eventually the annihilation reaction no longer takes place - the particle is said to freeze out. When this has happened, the number density of the particle remains constant - save for the natural dilution due to the expanding universe. The greater the thermally averaged cross sectionhσ_Avi, the longer the particles may annihilate. Therefore a greater annihilation cross section results in a smaller relic density. The Dark Matter density from section 1.1.3 thus gives bounds on the annihilation cross sections. Within the Minimal Supersymmet- ric Standard Model, constructing Neutralinos with a mass<20 GeV and sufficiently large annihilation cross section is possible, yet it requires a lot of fine-tuning of the free parameters [7]. Therefore, within this theory, neutralinos with masses between 45 GeV and 3 TeV are favored.

1.3 Direct Detection of Dark Matter

For this section and the remainder of this work, Dark Matter is considered to consist of WIMPs. Rotational curves of the galaxy suggest a Dark Matter distribution similar to ρχ ∼ r⁻². As a consequence, one expects a non-vanishing local Dark Matter density and thus the possibility to directly detect WIMP interactions here on Earth. An estimation of the expected WIMP flux through an earth bound detector and of the possible energy deposition is made to assess the feasibility of direct detection.

Variations of the exact halo profile will lead to different local Dark Matter den-

(12)

sities, yet amongst Dark Matter Experiments the value typically adopted is:

ρχ,local= 0,3·GeV /c²

cm³ (1.7)

Using a commonly assumed WIMP mass of 100 GeV, we can easily calculate the local number density as n_χ,local = 3·10⁻³/cm³. To obtain the flux through an earthbound detector, we consider the WIMPs to be stationary with respect to the Milky Way and our solar system moving through it at a velocity ofv_Sun= 220 km/s.

A simple multiplication yields the expected flux:

Φ_χ= 3·10⁻³

cm³ ·220km/s= 6·10⁵

cm²·s (1.8)

Only WIMP-nucleus scattering can transfer enough energy into a target to allow detection. The signal measured is the energy of the recoiling nucleus, the detection rate is given by:

R=n_T ·Φχ·σ(v) (1.9)

wheren_T is the number of target nuclei and σ the (unknown) WIMP-nucleus cross section.

The kinetic energy of an incident WIMP gives the upper bound for the maximum energy transfer. Assuming the velocity distribution of luminous matter and Dark Matter is similar, an average WIMP in our position will travel at: vχ = vSun = 220 km/s. In any case, an upper bound is given by the escape velocity of the Milky Way, which is around 544 km/s according to [8].¹ With these assumptions, the average kinetic energy of a 100 GeV WIMP is E_kin = 1/2mχv²_χ ≈ 50 keV. The whole kinetic energy can only be transferred in the case ofm_χ=m_T, where m_T is the mass of the target nucleus, and for complete back-scattering. These low energy signals require Dark Matter experiments to have an excellent energy threshold.

1.3.1 Expected Recoil Spectra

In equation 1.9, an expression for the total rate of WIMP-nucleus interactions was given. More information can be gathered by looking at the shape of the recoil spectrum. Several assumptions on the scattering process are made:

• Only elastic scattering will be considered

• Given their low energy, WIMPs are expected to generally scatter coherently off the entire nucleus, without probing its substructure. This gives a contribution of the target nuclei’s mass numberAin the scattering amplitude and a factor ofA² in the WIMP-nucleus cross section.

• The interaction is assumed to be spin independent.

1There are still large uncertainties contained in even the latest measurements of the galactic escape velocity. At 90% confidence level, the escape velocityvescis 498 km/s< vesc<608km/s.

(13)

Differentiating equation 1.9 (and expanding the expression Φχ), one obtains:

dR

dE_r =n_T ρχ

m_χ Z vesc

vmin

d³vf(~v)vdσ(~v, Er)

dE_r (1.10)

where f(~v) is the WIMP velocity distribution, which is generally taken as Maxwellian, with a cutoff at the galactic escape velocity. The differential cross section scales with:

dσ dEr

∼ A²

v²F²(Er) (1.11)

where F(Er) is the form factor, describing the spatial mass distribution of the nucleus. This becomes relevant at higher recoil energies, where the assumption of a coherent scattering process must be relaxed.² Putting this all together one arrives at:

dR

dE_r ∼n_TA²

µ²F²(E_r) Z vesc

vmin

d³vf(~v)

v (1.12)

whereµis the reduced mass of the WIMP nucleon signal and the integral evaluates to an expression∼e^−E^r. Summarizing, the differential rate gives great insight into the WIMP sensitivity of a setup. Particularly it should be noted that:

• The shape of the recoil spectrum is an exponential decrease, adjusted by the form factor at higher recoil energies.

• A higher rate is achieved by more target material as well as by nuclei with high mass number.

• The reduced mass term implies different recoil spectra for different WIMP masses and that experiments are most sensitive in the casemχ≈mT.

The recoil spectra of typical targets for a 100 GeV WIMP are shown in figure 1.3.

It is noticeable, that at recoil energies around 100 keV, the rate has dropped by many orders of magnitude in all targets. The diffraction minima in the xenon and tungsten curve reduce the interaction rate to almost zero for nearby energies. In the case of tungsten, less than 1% of all interactions are expected to have a greater recoil energy than 40 keV.

The effect of the WIMP mass on the recoil spectrum is shown in figure 1.4.

The base rates of the spectra drop with increasing WIMP mass. This is due to the reduced flux of WIMPs passing through the detector given a constant energy density. Also noteworthy, is that the rate of a 10 GeV WIMP almost vanishes at recoil energies exceeding 5 keV. An experiment with a tungsten target and an energy threshold above this value would thus have no possibility to detect such a WIMP.

2For a description of the various form factors and a detailed review of recoil spectra in general, see [9]

(14)

Figure 1.3: Recoil spectrum of 100 GeV WIMP in germanium, xenon and tungsten, which have atomic weights of 72.6 , 131.3 , and 183.8 respectively. The drop of the rates at very low energies stems from a non-zero energy resolution.

(15)

Figure 1.4: Recoil spectrum of various WIMPs in a tungsten target.

(16)

(17)

Chapter 2

CRESST

The aim of the “Cryogenic Rare Event Search using Superconducting Thermome- ters” is to detect WIMPs via their elastic scattering off nuclei in a target crystal.

Up to 33 crystals of the present geometry can be mounted in a modular structure to achieve a total target mass of up to 10 kilograms. A scintillating target is used, as this gives the possibility to actively discriminate possible WIMP signals from various background events. This is actualized by measuring a phonon and light signal in coincidence. The radioactive background from the surrounding is reduced by several shielding components. The chapter starts with an introduction of the employed detection principles and moves on to a description of the CRESST setup.

2.1 Cryogenic Detector Principles

Due to their low energy threshold and good energy resolution, cryogenic detectors are a good choice for detecting WIMP induced nuclear recoils. In principle, a thermometer measures the temperature increase caused by a particle interaction within a target crystal. The system is weakly coupled to a heat bath in order to restore the initial conditions within a reasonable time. Using a simple model, an energy deposition of ∆E in the target increases its temperature by:

∆T = ∆E

C (2.1)

where C is the heat capacity of the absorber. The increase in temperature is thus directly proportional to the initial energy deposition. The expected energy transfer from elastic WIMP-nucleon scattering is very small, in range of isO(keV). There- fore a measurable temperature difference can only be achieved by using a target with a very low heat capacity. At low temperatures, the electrons of dielectrics and semi- conductors cannot be excited thermally. The heat capacity is therefore dominated by the phonon contribution and scales as

C_ph∝ T

TD

3

(2.2)

(18)

where TD is the Debye temperature. In metals, the conduction electrons remain thermally excitable, giving an additional contribution to the heat capacity scaling with Ce ∝ T. CRESST currently uses 300 g CaWO4 crystals as absorbers, cooled down to about 10 mK. The temperature rise of such a crystal (i.e the phonon signal) is measured by a Transition Edge Sensor (TES) which is described in the following section.

2.1.1 Transition Edge Sensor

Superconductivity describes the phenomenon of the sudden loss of electrical resistance of a substance once it is cooled below a critical temperature TC. Around this critical temperature, the dependance of the resistance of the substance from the temperature (dR/dT) is very high. A Transition Edge Sensor uses this strong dependance, by stabilizing the temperature in the region of the phase transition.

CRESST uses tungsten films as TES, evaporated directly onto the target crystal.

The tungsten films have a typical thickness of 200 nm and a critical temperature TC in the range of 10−20 mK. A typical transition of such a tungsten film has a width∼mK and is shown in figure 2.1. A constant bias current across the tungsten film is used to measure the change of resistance following a particle interaction. The details of the readout will be discussed in section 2.1.2.

What has been omitted up to now is the coupling between the target crystal and the thermometer. An energy deposition in the crystal quickly leads to a population of high frequency phonons. The frequency distribution depends on the interaction type: Ionizing radiation, after the production of primary and secondary electron hole pairs, creates optical phonons. These decay into a monoenenergetic population of acoustical phonons with a frequency of ν = ν_D/2 in less than 1 ns. If the initial energy release follows a nuclear recoil reaction, acoustic, non-thermal phonons are created with a broad frequency range. In either case, these phonons start to thermalize within the absorber. This is a slow process, taking several milliseconds in which the non-thermal phonons can readily be absorbed by the electrons of the thermometer. The temperature of the electrons in the thermometer determine its resistance and thus the measured signal.

The coupling between the phonon and electron system of the thermometer Gep

is strongly temperature dependent (G_ep∼T⁵). At low temperatures this means the two systems are effectively decoupled, resulting in an overheating of the thermometer with respect to the absorber. In such a case, the heat capacity of the thermometer and the transport properties of the non-thermal phonons in the absorber determine the sensitivity.

After heating up, the thermometer relaxes via the connection to the heat bath.

In CRESST this is realized by a thin gold wire bonded onto the tungsten film. The relaxation timeτ is given by:

τ = CT

G_eb (2.3)

where CT denotes the heat capacity of the thermometer and Geb the coupling of

(19)

thermometer to heat bath.The coupling obtained should be strong enough, that the dead time of the detector doesn’t become too long after a high energy deposition.

A theoretical model of the pulse formation in CRESST detectors can be found in [10].

Figure 2.1: Transition curve of a typical tungsten film.

2.1.2 Readout

Figure 2.2 shows the basic readout circuit for CRESST detectors. A constant bias current I0 is supplied over two parallel branches, the tungsten thermometer in one, a reference resistor in the other. The reference resistor is arranged in series with the input coil of a SQUID ¹. A SQUID measures the change of magnetic flux and thus a change in current through the input coil. The current through the SQUID branch (I_S) is given by:

IS =I0· Rf(T)

R_f(T) +R_S (2.4)

where R_f(T) is the temperature dependent resistance of the tungsten film and RS

is the reference resistance. An energy deposition now results in an increase of the resistance R_f(T) and thus an increase in current in the SQUID branch.

The signal which enters the data acquisition system is supplied by the SQUID electronics. As already stated, SQUIDs measure changes of magnetic flux with great sensitivity. However, the response of a SQUID to a linear change in magnetic flux

1Superconducting Quantum Interference Device

(20)

Figure 2.2: Schema of readout circuit. A particle interaction heats up the thermometer and thus increases its resistance. This results in a larger current flowing through the input coil of the SQUID. Diagram taken from [11]

is periodic², oscillating with a period of φ₀. This φ₀ represents the magnetic flux quantum, that isφ0 =h/2e≈2·10⁻¹⁵Tm².

The output voltage of a SQUID VS to a magnetic flux from the input coil Φ is given by:

V_S =γ(Φ +nφ₀) (2.5)

whereγ denotes the gain of the system andnis an unknown integer. To resolve the ambiguity of the +nφ₀ term, an electronic feedback circuit keeps the flux through the loop constant. The current of the feedback circuit is used as the output signal.

In this way,nis set to a fixed value and the relation betweenV_S and Φ is linearized.

A constraint in this system is given by the ability of the feedback circuit to compensate the flux from the input coil. If the change in magnetic flux is too fast, it cannot be compensated by the feedback circuit and the value ofnin equation 2.5 changes. This phenomenon is called flux quantum loss.

2.2 Detector Modules and Active Background Discrim- ination

A crucial feature in the CRESST setup is the use of a scintillating target material.

If enough scintillation light is collected after a primary particle interaction, the

2For a review of the physical principles involved in a SQUID, see [12]

(21)

information can be used to distinguish common background events from possible WIMP signals.

2.2.1 Detector Modules

In order to measure both the primary phonon signal as well as the amount of scintillation light, a phonon detector as described in section 2.1 is paired up in a modular structure with a light detector.

Photomultipliers cannot be used to detect scintillation light at milikelvin temperatures as the photocathode eventually becomes non-conductive. In this case electron emission causes charging and consequently loss of sensitivity. Therefore, the CRESST collaboration has designed custom cryogenic light detectors for its detector modules. They consist of a light absorbing substrate onto which another TES is evaporated. The scintillation light following a particle interaction heats up the TES, the readout is analogous to the phonon channel. The scheme of such a module is shown in figure 2.3, a photograph in 2.4.

2.2.2 Scintillation quenching

Most of the background seen by CRESST detectors is eitherβ orγ radiation. These lose their energy in interactions with the electron shell of the target. Neutrons on the other hand scatter off the nuclei (in this case Oxygen, Calcium or Tungsten), losing most of their energy to oxygen due to kinematics. WIMPs, due to their large mass, are expected to only transfer measureable amounts of energy on to tungsten nuclei.³.

This all becomes relevant, as the scintillation efficiency for electron recoils is known to be significantly higher than for nuclear recoils [13]. Furthermore, the scintillation light is expected to be proportional to initial energy deposition for both electron and nuclear recoils [14]. With this information, it is clear that if one now plots the light versus the phonon energy of events in a scintillator, it should be possible to distinguish between electron and nuclear recoil events. An example of this is shown in figure 2.5

Apart from discriminating between electron and nuclear recoil events, the tech- nique of simultaneously measuring phonon and light signal can also distinguish between different recoiling nuclei of a composite target such as CaWO₄ . This is due to the fact that a heavier recoiling nucleus will produce a smaller fraction of scintillation light in comparison with a lighter nucleus. To quantify this behavior, the quenching factoris introduced. It is defined as:

QFX(Er) = Light produced by recoiling nucleus X of energy Er

Light produced by gamma of energy Er

(2.6) whereErdenotes the recoil energy transmitted onto nucleusX. For CaWO4 , the quenching factors of calcium, oxygen and tungsten have been measured repeatedly

3This is not the case for light WIMPs which are discussed in section 3.1.2.

(22)

within the CRESST collaboration. The newest results from [16] give values of:

• QF(Oxygen) = 11.1%

• QF(Calcium) = 6.4%

• QF(Tungsten) = 3.9%

Noticeable here is the small light output expected for all nuclear recoils as well as the small (absolute) difference. This makes it a challenging task to achieve the required resolution in the light channel to discriminate between the various nuclear recoils. Currently, not all nuclear recoil events can be unambigously identified.

Therefore a neutron background is very dangerous due to possibility of neutron induced oxygen recoils mimicking a tungsten signal. This will be further discussed in section 3.1.1.

2.3 Passive Shielding

Even though it has been shown that CRESST detectors can discriminate common background events from a possible signal, a very low background is still an absolute prerequisite. As the detectors require a comparatively long time to regenerate after a particle interaction, a too high background rate would cause significant dead time.

Furthermore, the separation of the various bands is not 100% efficient, especially at lower energies.

2.3.1 Radioactive Background

Background radiation can originate either from environmental radioactivity or from intrinsic sources within or close to the detector.

External gamma radiation stems mostly from the Uranium and Thorium decay chains as well as from⁴⁰K. It is shielded efficiently by high density targets with a high atomic number. In the CRESST setup, the gamma shield was realized by a 20 cm lead shield surrounding the detectors. As lead itself contains the unstable isotope

210Pb, a copper shielding of 14 cm thickness was installed between the lead and the detectors. The copper used was a special oxygen free high conductivity (OFHC) copper, which is an especially pure material with a very low intrinsic radioactivity.

Additionally, the detector modules are kept away from components of the setup with a higher radioactivity. An example of this is the dilution refrigerator which cools the detectors to their operating temperatures. In this case it does not encase the detectors, but conveys the low temperature via a 1.5m long cold finger.

Apart from external sources, interal radioactivity within the dector modules must be considered. As these obviously cannot be shielded against, one tries to reduce them by using only radiopure materials close to the detectors. Intrinsic radioactivity due to contamination of the crystals is the largest background seen by the CRESST detectors.

(23)

2.3.2 Neutrons and Muons

As mentioned in 2.2.2, neutrons pose a very dangerous background as event by event discrimination is not possible. Low energy neutron (some MeV) are produced mainly from (α, n) reactions or from spontaneous fission in the surrounding rock. To shield against these, a 45 cm layer of polyethylene was installed outside the lead and copper shielding. The many light hydrogen nuclei efficiently moderate the neutrons to thermal energies and thus below the detection threshold.

Muons, created in the atmosphere by cosmic rays, are very important to low background considerations. They can create background by either passing directly through the detector, through production of high energy electrons and consequent secondary particle showers or by interaction in surrounding material. This is particularly dangerous in the lead/copper shielding within the polyethylene, as neutrons may be produced in spallation reactions.

A great effort goes into reducing the experiment’s exposure to muons. As muons are highly energetic and penetrating, they cannot be stopped by ordinary shielding.

For this reason, the CRESST experiment is located in the the Laboratori Nazionali del Gran Sasso. This underground lab is located under 1400m of dolomite rock, reducing the muon flux by six orders of magnitude to roughly 2/m²h.

Even after this enormous reduction, muons still present a dangerous background.

Therefore, the CRESST experiment is equipped with a muon veto. It consists of 20 scintillator panels, covering a solid angle of 98.7%. If one or more of these panels triggers, the event is flagged to be muon induced and not used for Dark Matter analysis.

An idea of how the different components of the CRESST experiment are assem- bled can be gained by looking to figure 2.6.

(24)

Figure 2.3: Schematic of a detector module used in CRESST. The phonon and light detector are encased in a reflective housing to increase the amount of detected scintillation light.

(25)

Figure 2.4: Photograph of an opened detector module. The light detector is dis- played on the left, the phonon detector, consisting of CaWO₄ target with a thermometer evaporated on to it, on the right. The thermometer structure on the light detector is much smaller, due to the comparatively smaller signal and thus a required smaller heat capacity of the thermometer.

(26)

Figure 2.5: Scatter plots of the proof of principle detector module [15]. Both plots show the pulse heights of the light detector versus the phonon detector. The target crystal was irradiated with a ⁵⁷Co gamma and a ⁹⁰Sr beta source. For the right plot, an additional Am/Be neutron source was added. Both electrons and neutron induced events lie on distinct bands, the slope of which depends on the scintillation efficiency.

(27)

Figure 2.6: Schematic of the CRESST setup. Most of the volume is occupied by shielding components surrounding the detector modules.

(28)

(29)

Chapter 3

Search for Alternative Target Materials

An advantage of the CRESST experiment is that the setup can be left unaltered while exchanging detectors as well as target crystals. Therefore the CRESST collaboration has great interest into investigating alternative target materials to CaWO₄ . The main reasons for this are:

• Finding a material with a higher light yield at milikelvin temperatures to improve the resolution of the light channel. This directly leads to a lower energy threshold and raises the expected WIMP count rate.

• Improving the WIMP sensitivity by using a target with a favorable recoil spectrum.

• Looking into target materials without heavy nuclei dedicated to test light WIMP scenarios.

• Opening the possibility of detecting WIMPs in different targets, providing a convincing signature in the event of a dark matter signal.

These reasons will be further discussed in the following chapter, after which new potential target materials, CdWO₄ and Al₂O₃:Ti are introduced. An introduction into scintillation mechanisms is also given.

3.1 Motivation

3.1.1 CRESST sensitivity and the light channel

As was discussed in 2.2.2, events are separated into distinct bands in a light versus phonon plot. These bands have a certain width, which is determined by the energy resolution of both channels, the light channel contributing dominantly. Figure 3.1 shows the electron, oxygen and tungsten band with an energy resolution typical for CRESST detectors . It is noticeable, that up to 12 or 13 keV, the electron band

(30)

overlaps with the nuclear recoil bands. This makes all events with a lower energy unusable for Dark Matter analysis. Henceforth, the energy above which electon recoils can be separated from nuclear recoils with a sufficiently high efficiency will be referred to as the energy threshold. Furthermore, the oxygen and tungsten band overlap in parts over the signal energy range. This makes it crucial to the experiment to either eliminate or fully understand a possible neutron background. Both are difficult tasks and make the analysis of the results a very challenging undertaking.

Figure 3.1: Electron,oxygen and tungsten bands in the light/phonon plane. Energy resolution typical for current CRESST detectors[14]. There is a large overlap of all bands at low energies.

Figure 3.2 shows the quasi optimal situation, in which the energy resolution of the light channel has been improved by a factor of five. The electron band overlap stops at about 2 keV, dramatically improving the threshold. The effect on the Dark Matter sensitivity of the experiment is even greater considering exponentially de- creasing recoil spectrum of WIMPs. Another nice feature is that above 15 keV the oxygen and tungsten band are completely separated. This means that above this energy a neutron background could be unambiguously identified and the danger of it mimicking a WIMP signal is eliminated. This only holds in the case of all neutrons scatterings with energy above the threshold are with oxygen and all WIMPs with tungsten.

There are many factors determining the resolution of the light channel.¹ These

1A comprehensive description of the light channel and the factors determining its resolution can be found in [14].

(31)

Figure 3.2: The same diagram as figure 3.1, but with the resolution of the light channel improved by a factor of five. The events are focuses into more narrow bands, the discrimination is efficient at significantly lower energies.

include the probability of created photons to reach the light absorber; the absorption probability of the photons in the light absorber; the phonon transmission and subsequent absorption efficiency in the thermometer as well as several noise sources.

The most obvious factor is naturally the number of scintillation photons created in the first place. Therefore the main focus of this work was the investigation of the light yield of new target materials at low temperature.

3.1.2 The Light WIMP Scenario

One of the few positive Dark Matter claims comes from the DAMA collaboration.

The employed detection principle consists of measuring the scintillation light of highly radiopure NaI:Ti within a low background setup. The collaboration presents the interesting results of an observed annual modulation (see figure 3.3) of the signal in the low energy range. At higher energies the modulation disappears as would a potential Dark Matter signal. The period of 1 year, as well as the phase, nicely match the expected modulation caused by the Earths movement through the galactic Dark Matter halo.

The reason why the DAMA claim has not settled the issue on Dark Matter is that the most sensitive experiments in the field have so far exclusively provided null

(32)

Figure 3.3: Annual modulation as seen by DAMA. The continuous line represents the expected modulation of a Dark Matter signal with period of one year and the correct phase. The amplitude of the modulation was fit to the data points. Diagram from the most recent results paper of the collaboration [17]

results.² This means that the DAMA result cannot be explained by Dark Matter particles within the expected mass range scattering elastically within the target.

Apart from inelastic scattering scenarios, light WIMPs with masses ∼10 GeV can be constructed in non-minimal supersymmetric theories and would reconcile the results [7].

CRESST is in the comfortable situation that the current CaWO4 target is already sensitive towards such WIMPs due to the oxygen nuclei. Additionally, a different target consisting only of light nuclei could further increase the sensitivity towards light WIMPs.

3.2 The Basics of Scintillation

The mechanism of scintillation, in which ionizing radiation is partially converted into visible light can be described in five distinct steps [19].

1. Absorption of a high energy particle, creating a primary electron as well as an inner shell hole.

2. Creation of secondary electron hole pairs. These can be excited by X-rays, Auger electrons or inelastic electron/electron scattering.

3. Thermalisation. When the energies of the secondary electrons is lower than the ionization threshold, further electron hole pairs cannot be created. Electrons

2An example of this is the recent result of the CDMS II collaboration [18]

(33)

thermalize to the bottom of the conduction band, holes to the top of the valence band.

4. Energy transfer of the electrons and holes to the luminescence centers.

5. Radiative decay of the excited luminescence centers.

The whole process is illustrated in figure 3.4. The efficiency of the process is characterized by the number of photons N_ph produced per energy deposited by the incident particle, E_dep

Nph=N_e/hSQ= E_dep

E_e/hSQ (3.1)

Here, N_e/h is the number of secondary electron hole pairs created. The average energy required to create such an electron hole pair E_e/h. This energy is typically between two and three times the band gap of the material. The other quantities in equation 3.1, S and Q, denote the efficiency with which electrons and holes are transported to, and excite, the luminescence centers, as well as the quantum efficiency of a luminescence center.

In an extrinsic scintillator the luminescence centers are introduced via a dopant.

Such a scintillator was assumed in figure 3.4, where the energy levels of the dopant are indicated between valence and conduction band. The energy levels of the dopant can be used to estimateQ. Specifically, if the energy gap between the dopant ground and excited state is small compared to the energy gap of the scintillator, much of the recombination energy of an electron hole pair will be lost in non-radiative processes.

Conversely, if the excited state of the dopant is too close to the conduction band, an electron in the excited state may easily be raised back into the conduction band.

The electron hole pair may then decay in a non-radiative process.

The quantityS, describing the efficiency of energy transfer into the luminescence centers is only poorly understood. It includes different non-radiative processes and is dependent on many parameters, including temperatures and impurities. Lattice defects may trap electrons and holes, preventing them from exciting luminescence centers and therefore quenching the scintillation.

3.3 New Target Materials

New target materials must fulfill certain criteria in order to be viable for use within the CRESST experiment. These include:

• The material be dielectric, to ensure a low heat capacity at low temperatures.

• A high light yield at low temperatures, preferably better than CaWO4 .

• No surface effects in order to prevent a position dependency of the light yield.

• A low intrinsic radioactivity.

(34)

Figure 3.4: Basic scheme of the scintillation mechanism. The recombination of a thermalized electron hole pair is not shown, even though it is an allowed process.

The produced photon will be reabsorbed however, therefore this process does not contribute to the scintillation. Diagram taken from [19].

• At least one heavy nucleus if the aim is to test for heavy WIMPs or a high density of light nuclei if the aim is to test for light WIMPs.

This study focuses on Cadmium Tungstate (CdWO₄ ) and on titanium doped sapphires (Al2O3:Ti ), which were investigated specifically concerning their light yield at low temperatures.

3.3.1 Cadmium Tungstate

Measurements at room temperatures and at 9 K have shown that the light yield of CdWO₄ to be up to 140% of that of CaWO₄ [20]. This, together with its high density of heavy nuclei, motivate further enquiry into the suitability of CdWO4 as a prospective target for Dark Matter searches. In this section, the physical properties of CdWO₄ will be compared with those of CaWO₄. A closer look will be taken at the effects of the intrinsic radioactivity of cadmium. Finally, the results of evaporating a TES on a sample CdWO4 crystal are presented.

Physical Properties

Table 3.1 lists various relevant physical properties of CdWO4 as well as of CaWO4 . One notes the different structure, which results in slightly closer packing of the CdWO4 nuclei. Combined with the large mass difference of cadmium and calcium,

(35)

Properties CaWO4 CdWO4

Density [ g/cm³] 6.06 7.90

Melting point 1650^◦C 1325^◦C

Structure Sheelite Wolframite

Maximum of emission spectrum 420 nm 480 nm

Refractive index 1.94 2.25

Average decay time (at 20^◦C) 8µs 13µs

Table 3.1: Comparison of several key properties of CaWO4 and CdWO4 . Data taken from [21] and [22]

.

this results in a considerable density difference between the substances. The impor- tance of this is discussed further in section 3.3.1.

The different structure, also result in different scintillation centers and thus different emission spectra. The emission spectrum is important for two reasons. Firstly, the efficiency of the light absorber and the efficiency of the reflective foil are wave- length dependent. Thus a good match between these two functions and the emission spectrum are favorable for the light collection. The second argument is simple photon statistics: The light energy detected obviously depends on the number of primary created photonsn_ph and their mean energy E_ph:

EL∼nphEph (3.2)

Taking the width of a light peak in first order to be ∆EL∼√

nphEph this gives an expression for the resolution of:

∆E E ∼ 1

√n_ph ∼ s

E_ph

E_L (3.3)

What is important here, is that even if two scintillators emit the same amount of light energy, an emission spectrum shifted to higher wavelengths will increase the resolution of the light channel. Due to this effect, a setup using a CdWO4 target will have the resolution of the light detector improved by ∼ 5% compared with a setup containing a CaWO4 target of the same light yield.

Another interesting optical property is the refractive index. It is important, as light created in the target crystal, necessarily has to leave the crystal before it has a chance to be detected. If scintillation light approaches a crystal with a too shallow angle, it will be totally reflected back into the crystal. The angle of incidence, above which total reflection occurs is called the critical angle (θ_C) and is given by the equation:

θ_C =arcsin( n_air ncrystal

) (3.4)

This gives critical angles of 26.4^◦ for CdWO₄ and 31.0^◦for CaWO₄ . Obviously, a smaller critical angle means a higher chance of total reflection at the crystal surface.

(36)

Other factors must be considered however, if one wants to estimate the effect of internal reflection on the light signal.

The first is the absorption length of the scintillation light in the crystal. The second is the geometry of the crystal. A cylindrical geometry as used in the CRESST setup is highly symmetrical and can easily trap photons indefinitely. More irregular geometries are favorable to ensure that photons traveling on infinite trajectories within the crystal are less likely. A quantitative analysis of the effect of different geometries was done within [23] for CaWO₄ , with the result that a cubic geometry could decrease this self trapping by more than a factor of two. The factor of possible improvement would be even higher for CdWO4 , where self trapping is more likely due to the higher refractive index.

Intrinsic Sensitivity

In section 1.3.1, recoil spectra of single nuclei targets were introduced. However, in a composite target, all nuclei can potentially receive recoil energy from WIMPs and contribute to the signal. Figure 3.5 shows the recoil spectra for oxygen, calcium, cadmium and tungsten assuming a WIMP mass of 100 GeV. It illustrates that the implicit assumption of only needing to consider tungsten in a CaWO₄ target for Dark Matter analysis was justified (in this WIMP mass range). This however is not true for CdWO4 , where one would expect a sizable fraction of the signal from cadmium recoils. It is noticeable that the cadmium spectrum is considerably more flat than the tungsten spectrum and the sensitivity for Dark Matter-induced nuclear recoils is therefore not quite as dependent on a low energy threshold.

Next, one would like to compare the two targets in terms of their WIMP sensitivity. For this, one has to sum the correctly weighted recoil spectra of the constituent nuclei and integrate these up starting from the energy threshold. Here it is important to compare targets of equal volume and not of equal mass, as this is the experimental constraint. The intrinsic sensitivity of a composite target is defined as

Intrinsic Sensitivity:=X

i

Z ∞

Ethr

ρ_idR_i

dE_r(m_χ)dE_r (3.5) where_dE^dRⁱ

r are the differential recoil spectra of the nucleusi, as calculated by equation 1.10 andρ_ithe mass density. The remaining free parameters are the energy threshold as well as the WIMP mass.

Figure 3.6 shows the effect of the energy threshold on the intrinsic sensitivity of CdWO4 and CaWO4 for various WIMP masses. As expected from the cadmium contribution as well as the higher density, cadmium tungstate yields a higher sensitivity, especially for higher thresholds. CRESST detectors typically have an energy threshold between 10 and 20 keV.

Next, the sensitivity with respect to the WIMP mass is analyzed. For this, a hypothetical experiment is performed in which a CaWO₄ and CdWO₄ target of 1000 cm³ is exposed for a day in a background-free experiment, with an energy

(37)

Figure 3.5: Recoil spectrum of the constituent nuclei of calcium and cadmium tungstate for a 100 GeV WIMP. Spectra normalized to account for different mass fractions of each element within both compounds.

threshold of 10 keV. The assumed result of this experiment is that no signal events are observed. The question that remains is - what could be learned from such a result?

Given two specific values of WIMP mass and WIMP-nucleon-cross-section, it is possible to calculate the expected number and energy spectrum of signal events, for a given target and exposure. These can then be compared with the actual measured events. If the expected number is significantly higher than the measured number, the assumed (WIMP mass, WIMP-nucleon-cross-section) - pair can be excluded. In an exclusion plot, the lowest excluded cross section is shown as a function of the WIMP mass. It is customary to exclude cross sections with 90% confidence, meaning that in 90% of a large number of identical experiments, the ’true’ WIMP-nucleon- cross-section will not be falsely excluded.

In our hypothetical experiment, cross sections would be excluded down to the point at which less than 90% of identical experiments would be expected to show a

(38)

Figure 3.6: Ratio of the intrinsic sensitivities of CdWO₄ and CaWO₄ for different WIMP masses as a function of the energy threshold. For a CRESST-typical energy threshold of 10-20 keV, the expected WIMP count rate in a CdWO4 target is higher by a factor between 1.5 and 2.

signal.³ The exclusion plots of our hypothetical experiment performed are shown in figure 3.7. CdWO4 excludes a greater parameter space over the entire WIMP mass spectrum. This is slightly surprising, as for low WIMP masses one would expect the light calcium nuclei to tilt the scales in favor of CaWO4 . However, the higher number density of nuclei in CdWO4 compensates this.

Intrinsic Background

A reason why CdWO₄ has so far not been considered for the CRESST Dark Matter search, is cadmium not being considered a radiopure element. Natural cadmium typically contains 12.22% of the unstable isotope ¹¹³Cd [25]. It has a half-life of 9.3·10¹⁵y and decays via beta decay into the stable¹¹³In. The Q-value of the decay is 316 keV , the energy spectrum of the emitted electron is shown in figure 3.8. It

3In a realistic scenario, one has to consider a combination of known and unknown background, as well as possible signal events. The methods to extract limits in such a case are more complicated and beyond the scope of this work. A general method for low count experiments is introduced in [24], the implementation for CRESST is discussed in [9]

(39)

Figure 3.7: Exclusion plots of our hypothetical experiment. A lower cross section is excluded by the CdWO4 target across the entire WIMP mass spectrum.

adds a relatively featureless background over the entire region of interest. In principle this can be handled, as the separation of electronic and nuclear recoils works with very high efficiency. However the additional dead time has to be considered. In a cylindrical crystal of height and diameter of 40 mm as used in CRESST, the rate of

113Cd decays is calculated to be 0.23 s⁻¹. Considering the standard record length is 328 ms, roughly 8% of the measurement time will be lost due to these decays.

Another source of possible background are trace impurities in the cadmium. In [26], the trace impurities of high purity cadmium were analyzed using inductively coupled plasma mass spectrometry. A contamination of Samarium in the range of 0.1−0.2 ppm was detected in both analyzed samples. Naturally occurring samarium contains 15% of the unstable isotope ¹⁴⁷Sm, which alpha decays with a half life of 1.06·10¹¹ain to ¹⁴³Nd . The rate of this decay in a CRESST sized CdWO4 crystal would be around 0.5/min. With a Q-value of 2.3 MeV the decay occurs far away from the signal region. However, the case must be considered, in which the the decay happens on the crystal surface and the alpha leaves the crystal undetected. This is a potentially very dangerous background, as a heavy nucleus such as the Neodymium will be indistinguishable from a tungsten recoil for all practical purposes. From

(40)

decay kinematics, one can calculate the kinetic energy of the¹⁴³Nd to : Ekin,N d = Q

1 +^m_m^{N d}

α

= 64.5 keV (3.6)

wherem_Ndis the mass of the¹⁴³Nd nucleus andm_α the mass of the alpha particle.

This background is thus very close to the signal region.

Assuming that the contamination is not localized at the surface, one can estimate the rate of this background. The background is dangerous if the alpha does not deposit any or enough energy in the crystal. The stopping power of alpha particles in CdWO4 is dominated by the oxygen atoms and is roughly 1.73 GeV/cm [27]. If one judges the background as ’harmless’ once the alpha particle deposits more than 50 keV in the crystal, then only decays within 3·10⁻⁵cm of the surface must be considered. In a cylindrical crystal of size (φ40×40) mm³ this would be a volume fraction of∼2·10⁻⁶. As in one half of these cases the alpha particle will be emitted into the crystal, this means that in about every millionth ¹⁴⁷Sm decay, the alpha would leave the crystal potentially undetected. This translates into an acceptable rate of∼0.5/year.

Figure 3.8: Energy spectrum of the electron emitted in a¹¹³Cd decay [28]. Within the region of interest it adds a relatively flat background.

(41)

TES on Cadmium Tungstate

In most of the detector modules currently used in CRESST, the thermometer used for the phonon signal is evaporated directly onto the target crystal.⁴ As was ex- pressed in section 2.1.1, CRESST uses a superconducting tungsten film as a Tran- sition Edge Sensor (TES) for this purpose. For a phonon detector it has a typical thickness of 200 nm and covers an area of 5.9×7.5 mm². Aluminium and gold struc- tures are also evaporated and sputtered onto the tungsten film respectively, the scheme is shown in figure 3.9.

Figure 3.9: Scheme of the TES. Diagram taken from [30]

The aluminium stripes are used as electrical contact pads for measuring the resistance change of the tungsten film. The tungsten film is biased using Al wires (∅25µm) bonded directly onto these contact pads. The gold stripe is necessary for regulating the temperature of the thermometer. This is achieved by two components. The first is the thermal link, which cools the crystal and thermometer below the superconducting transition. The second component is the heater circuit, with which the thermometer can be heated to a temperature within its transition. The temperature stabilization is discussed in section 4.2.2.

Bulk tungsten has a critical temperature of 15 mK at which it becomes superconducting. Evaporating a thin film of tungsten which retains thisTC requires lots of experimental expertise, as the critical temperature of tungsten is very sensitive to magnetic impurities as well as towards the crystal structure [31]. Magnetic impurities are dangerous, as a concentration of ∼ 1 ppm can reduce the TC of a film

4The viability of evaporating a TES onto a small crystal and gluing it onto the large target crystal was shown in [29]

(42)

by 1 - 10 mK. With a ’base’ TC of 15 mK, these can easily suppress superconductivity completely. The crystal structure is important, as only tungsten with a b.c.c structure has aTC of 15 mK. Impurities can cause tungsten to crystallize differently, leading to a critical temperatures higher than 4K.

Over the years, much experience has been gained at the Max-Planck-Institute for Physics in the process of evaporating thin tungsten films onto CaWO₄ crystals.

Without a change in the procedure, a 200 nm tungsten film was evaporated onto a sample CdWO₄ crystal of size (5×10×20) mm³. The measured transition curve of the produced film is shown in figure 3.10. The transition temperature is 21.5 mK, low enough for a cryogenic detector. The transition curve shows deviations from an idealized curve. Specifically it looks like the superposition of two areas of film with aT_C difference of about 2 mK. This suggests a local impurity concentration increase in parts of the film.

Figure 3.10: Transition curve of the TES evaporated on a CdWO4 crystal.

3.3.2 Titanium Doped Sapphire

In section 3.1.2, the investigation of a target material specifically sensitive to light WIMPs was motivated. For this purpose, titanium doped sapphire (Al2O3:Ti ) was chosen. The CRESST collaboration already has some knowledge in dealing with sapphires, as this was used as a target in the first phase of the experiment when only a phonon signal was measured [32]. This expertise is advantageous, specifically concerning the knowledge acquired in using it as a phonon detector. Furthermore, sapphire was shown to be a highly radiopure substance.

(43)

In this chapter, an overview of the previous research on the optical properties of Al₂O₃:Ti will be given. The intrinsic sensitivity to light WIMPs will be discussed.

Scintillation Properties

The scintillation properties of Al₂O₃:Ti have been studied in the context of dark matter searches by [33] and [34]. It has been shown that the concentration of the titanium dopant affects the scintillation, albeit in a complicated way. Nominally pure Al₂O₃ has also been shown to be good scintillator with a light yield of 1.3%

measured by [19].

Much can be learned by comparing the luminescence spectrum of Al2O3:Ti at various titanium concentrations, seen in figure 3.11. It shows, that several competing processes lead to the emission of scintillation light. The spectra are dominated by a wide emission band at around 750 nm. It occurs due to an electronic transition of aT i³⁺ ion. The intensity of this particular emission band increases for titanium concentrations up to 100 ppm and decreases for higher concentrations. The same behavior is seen in the emission band at 300 nm. Here, the origin of the luminescence is thought to be due to electron hole pairs, being trapped atT i³⁺ ions [35]. At this position, the band gap between conduction and the valence band is reduced, so that the recombination of the electron hole pair produces a photon which is not reabsorbed. It is important to note, that in both emission bands, theT i³⁺ ion plays the decisive role. However, as a dopant in Al2O3, titanium also forms T i⁴⁺ ions.

Thus the concentration of T i³⁺ ions, not the simple titanium concentration, is the relevant quantity in scintillation studies.

A third emission band at 410 nm is seen for the sapphires with the lowest concentration of dopant. It is thus likely, that such an emission occurs in pure Al₂O₃. In pure Al₂O₃, luminescence occurs in the so-called F-centers, which are oxygen defects occupied by either one or two electrons. The fact that this emission disappears for higher dopant concentrations, suggests that the excitation efficiency of the F-centers is comparatively low.

It should be said, that the final word on the scintillation mechanism of Al2O3:Ti has yet to be spoken. Especially the nature of the blue emission band at 410 n is still being debated. Therefore, what was presented in the last paragraphs is at best a rough approximation and at worst simply incorrect. Furthermore, different trends concerning the light yield of Al₂O₃:Ti have been measured. [33] reports a quasi constant light yield, varying by only 20% between various Al₂O₃:Ti crystals with a dopant concentration ranging between 10 and 1000 ppm. Conversely, in the measurement of reference [34], the light yield of a 75 ppm sapphire was more than twice that of a sapphire with a titanium concentration of 10 ppm.

All of this leads to the conclusion, that further measurements of the light yield of doped sapphires are necessary. Measurements with different, known T i³⁺ concentration are necessary to gain further insight into the scintillation characteristics of Al2O3:Ti .

(44)

Figure 3.11: Luminescence spectra of various Al₂O₃:Ti , irradiated with X-rays at room temperature [33]

Sensitivity for low mass WIMPs

A sapphire target, containing no heavy nuclei, naturally only offers limited sensitivity towards WIMPs with masses &50 GeV. For low WIMP masses however, a target containing only light nuclei may be favorable though. For an identical hypothetical experiment as was done in section 3.3.1 the exclusion plots are shown in figure 3.12.

From this one can see, that for WIMPs lighter than 17 GeV, a Al₂O₃ target offers a higher sensitivity. For anything above 30 GeV however, the sapphire target fares worse by an order of magnitude. Given the newest CRESST results [9], a Al₂O₃:Ti target with a high enough light yield might however be of great interest.

(45)

Figure 3.12: Exclusion plots for CaWO4 and Al2O3 target in the low WIMP mass range. Different from the exclusion plot in figure 3.7, the mass is not presented on a logarithmic scale.

(46)