Analysis of defect formation in semiconductor cryogenic bolometric detectors created by heavy dark matter
Highlights
► Formation of defects in cryogenic detectors due to WIMPs interactions is analysed. ► Luke–Neganov effect is extended to consider the energy stored in defects. ► The energy of WIMPs recoils is partitioned in ionization, phonons and defects. ► Consequences of defect formation for detection are analysed.
Introduction
In the last decades, great developments in low temperature detectors in the form of bolometers, in the technologies of semiconductors, superconductors or scintillator crystals were obtained. These cryogenic detectors are able to detect radiations and particles with a threshold in the range of eV.
If the pioneering idea of the bolometric detectors goes back to 1935, year when Simon suggested an “Application of Low Temperature Calorimetry to Radioactive Measurements” [1], the modern applications started after the ’70. Nowadays, there are a lot of reviews in this thematic: see for example those of Gaitskell [2] and Sarazin [3]. Bolometric detectors are used in different applications in experimental physics, e.g. in searches for neutrinoless double beta decay and neutrino mass – for example the experiments CUORE & Cuoricino, for total energy measurements of free electron lasers [4], to measure the cosmological microwave background [5] constituents of the dark matter, etc.
There is clear evidence that a large part of the dark matter in the Universe is non-baryonic, non-luminous and non-relativistic and the search for it has become a very active research area in the last decades. Hypothetical Weakly Interacting Massive Particles (WIMPs) are proposed as possible particle candidates that satisfy all of the above criteria. Thus, their direct detection using the experimental information of low-energy nuclear recoils originating from WIMPs interactions is one of the detection methods usually used in bolometric detectors.
If in the first generation of these experiments only the heat deposited in detectors as phonons was used in the detection, in more recent experiments phonons and ionization (or light from scintillation signals) are measured simultaneously, trying to discriminate both between electron – nucleon/nuclei recoils and also between different sources of the phenomena: ordinary matter or constituents of the dark matter. As detector materials, silicon and germanium or scintillator crystals (Al2O3:Ti or CaWO4, CaMoO4 etc.) are used.
One of the effects produced by the slowing down of particles in crystalline semiconductors is defect production, which is a phenomenon present at all temperatures. Defect formation after electron and gamma irradiation at temperatures around and lower than liquid He was studied in InP, Si, Ge, and SiC since 1995 [6], [7], [8].
In this paper we discuss the effects introduced in the energy balance by the formation of long time stable defects in materials for bolometers and possible consequences for the identification of the particles. In the next section, general aspects related to defect formation in the process of slowing down of selfrecoils in silicon and germanium are reviewed, with emphasis on the existing experimental data related to defect formation following cryogenic irradiation. The energy stored in Frenkel pairs is calculated, and the formulae relating it to the measured quantities in heat and ionization detectors are derived. Concrete applications related to direct WIMPs searches with these detectors are discussed, underlying the influence of the energy stored in defects.
Section snippets
Energy balance in heat and ionization cryogenic detectors
After the primary interaction of an incoming particle in the semiconductor, a selfrecoil of energy E is left. It loses energy in both electronic and nuclear collisions.
Let be the energy deposited in the semiconductor in the form of atomic collisions, and the total energy given to the electronic system, both calculated using Lindhard’s theory [9]. Part of the energy is stored in lattice defects (ED), the other part being given to the lattice in the form of excitations (phonons).
If
Physical processes related to WIMPs direct detection
The nature and characteristics of DM is a question of central importance in cosmology, astrophysics and astroparticles. The list of candidates and the possible signatures of DM have greatly expanded due to recent experimental results and observations [34], [35]. A summary of dark matter particle candidates, their properties, and the potential methods for their detection was recently given in Refs. [36], [37]. WIMPs are the most studied from all DM candidates, are found in many particle physics
Results and discussion
In the discussion which follows, a WIMP with mass in the range 5–100 GeV, having a velocity of 260 km/s in respect to a terrestrial detector is considered. It has a single interaction in a Ge or Si cryogenic detector.
For silicon, the first result of the energy partition between ionization and other processes using the complete Lindhard theory was obtained by Lindhard and later published in the paper of Simon [45]. Analytical approximations of the Lindhard equations both for silicon and germanium
Summary
The possibility of defect formation in bolometric semiconductor detectors at cryogenic temperatures was studied, with application to WIMPs direct searches.
The models for the partition factor between the energy transferred by the primary recoil to the atomic and electronic systems of Si and Ge were reviewed, starting from Lindhard’s theory. Part of the energy transferred to the atomic system is stored in defects. At sub-Kelvin temperatures the defects are Frenkel pairs and they do not anneal out.
Acknowledgment
MLC and SL thank the NIMP Core Programme PN09-450101 for financial support.
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