We present a detailed characterisation of the new Hamamatsu R12199-01 HA MOD 3-inch photomultiplier tube (PMT) which is under consideration for the use in segmented optical modules of deep-ice neutrino detectors at the South Pole. Because of the significantly lower operation-temperature range compared to standard applications, a focus of our studies lies on the investigation of the temperature dependence of background characteristics (dark count rate, probability of correlated pulses), timing properties, gain and peak-to-valley ratio of this PMT type. In addition, the performance of the `HA coating intended for background reduction was tested, as well as the influence of conductive objects near the photocathode like reflectors on the PMT noise rate. A low background rate is of particular importance as the deep ice at the South Pole features negligible optical background. We find that the new PMT type is well suited for the intended applications.
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