The structure and electrical properties of CdTe Schottky diode X/γ-rays detectors fabricated by DC reactive magnetron sputtering of Ti on the surface of semi-insulating p-like CdTe single crystals have been investigated. At relatively low voltages, the current transport processes in the Ti-TiOx/p-CdTe/MoOx-Mo structure are well described in the scope of the carrier generation in the space-charge region and space-charge limited current models. The charge carrier lifetime, energies of generation-recombination centers and hole traps, and density of discrete trapping centers were determined by comparing the experimental and calculation data. Because of the presence of a thin intermediate insulator layer in the p-CdTe/MoOx-Mo contact, a rapid increase in the reverse current due to the Poole-Frenkel emission is observed. The results obtained from the measurements of the I-V characteristics and model of space-charge limited current incorporating the Poole-Frenkel effect are compared and discussed.