Ohmic CdZnTe and CdTe detectors have been successfully used in high-energy missions such as IBIS on-board INTEGRAL and the Swift-BAT in the past two decades. Such detectors provide very good quantum efficiency in the hard X-ray band. For the future generation of hard X-ray coded mask detectors, a higher sensitivity will be required. A way to achieve this is to increase the effective area of the pixilated detection plane, to change the mask pattern and/or the properties of the semi-conductors paving the detection plane. For the future Chinese-French Gamma-ray burst mission SVOM, the GRB trigger camera ECLAIRs will make use of a new type of high-energy detectors, the Schottky CdTe detectors. Such detectors, when reversely biased, are known to present very low leakage current, resulting in lower values of the low-energy threshold (down to 4 keV or less) than for previous missions (i.e. > 10 keV for the Swift-BAT and INTEGRAL/IBIS). Such low values will enable ECLAIRs with a moderate geometrical area of 1024 cm2 and a low-energy threshold of 4 keV to be more sensitive to high-redshift GRBs (emitting mainly in X-rays) than the Swift-BAT with a higher effective area and low-energy threshold. However, the spectral performance of such detectors are known to degrade over time, once polarized, due to the polarization effect that strongly depends on the temperature and the bias voltage applied to the detectors. In this paper, we present an intensive study of the properties of Schottky CdTe detectors as used on SVOM/ECLAIRs such as I-V characteristics, polarization effect, activation energy and low temperature annealing effects. We discuss the implications of these measurements on the use of this type of detectors in future high-energy instruments.