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Thallium bromide (TlBr) is a compound semiconductor characterized with wide band-gap energy (2.68 eV), high atomic numbers (Tl: 81, Br: 35) and high density (7.56 g/cm3). Therefore, TlBr is a suitable material for fabrication of X- and gamma-ray detectors. In this study, TlBr detectors have been fabricated from the crystals grown by the traveling molten zone method. The detectors have thickness of approximately 0.4 mm, and have gold electrodes (3 mm in diameters) on both surfaces of the crystals. In order to evaluate the temperature dependence of the charge transport properties of the detectors, the mobility-lifetime products for electrons ((mutau)e) and holes ((mutau)h) in the detectors have been estimated by the Hecht analysis at various temperatures of the detectors (-40, 20, 0, 20 and 40 degC). The (mutau)h in the detectors was of the order of 10-5 cm2/V at -40 degC, and increased with increasing temperatures. The maximum value of the (mutau)h was obtained at 20 degC, and was about ten times larger than the value at -40 degC. On the other hand, the (mutau)e was approximately 1 times 10-3 cm2/V between -40 degC and 20 degC. The temperature dependence of spectral response of the detectors has been evaluated by acquiring energy spectra of gamma-rays from 241Am at -40, 20, 0, 20 and 40 degC. At -40 degC, the full-energy peak corresponding to 59.5 keV gamma-rays has been obtained from the detectors, but the energy resolution of the peak was degraded due to the hole tailing on the low-energy side of the peak. The energy resolution of the detectors gradually improved with increasing temperatures of the detectors. The best FWHM energy resolution was measured to be 5.4 keV (9.1 %) at 20 degC.