Development of cryogenic low background detector based on enriched zinc molybdate crystal scintillators to search for neutrinoless double beta decay of $^{100}$Mo

ZnMoO$_4$ scintillators with a mass of $\sim$ 0.3 kg, as well as Zn$^{100}$MoO$_4$ crystals enriched in the isotope $^{100}$Mo were produced for the first time by using the low-thermal-gradient Czochralski technique. The optical and luminescent properties of the produced crystals were studied to estimate the progress in crystal growth quality. The low-temperature tests with a 313 g ZnMoO$_4$ and two enriched Zn$^{100}$MoO$_4$ crystals were performed aboveground in the Centre de Sciences Nucléaires et de Sciences de la Matière. The low background measurements with a three ZnMoO$_4$ and two enriched detectors installed in the EDELWEISS set-up at the Laboratoire Souterrain de Modane were carried out. To optimize the light collection in ZnMoO$_4$ scintillating bolometers, we have simulated the collection of scintillation photons in a detector module for different geometries by Monte Carlo method using the GEANT4 package. Response to the 2$ν$2$β$ decay of $^{100}$Mo was simulated for the enriched Zn$^{100}$MoO$_4$ detectors of different shape and mass to understand the dependence of 2$ν$2$β$ decay spectra on crystal shape. We have simulated 48 Zn$^{100}$MoO$_4$ crystals with a size of Ø60 $\times$ 40 mm installed in the EDELWEISS cryostat. The contribution to background from the internal radioactive contamination of the crystals, cosmogenic activation and radioactive contamination of the set-up were simulated. Taking into account poor time resolution of the low temperature bolometers, we also studied contribution to background at the Q$_{2β}$ energy of random coincidences of signals, in particular of 2$ν$2$β$ decay, which is one of the main sources of background in cryogenic bolometers. Methods of the randomly coinciding events rejection were developed and compared. We have also analyzed dependence of the rejection efficiency on a cryogenic detector performance.

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