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Charge transport mechanism in X- and γ-ray detectors based on CdTe diodes with a p-n junction is studied. Shallow p-n junctions were formed in semi-insulating p -like CdTe crystals by laser-induced doping of a thin semiconductor layer with In atoms and, finally, In/CdTe/Au diode structures were fabricated. The energy diagram was developed to explain the reverse I-V characteristics of the diodes particularly increased leakage current. It was shown that the I-V characteristics at low bias voltages were described by the Sah-Noyce-Shockley theory. At higher voltages, an additional increase in leakage current was observed and it was attributed to injection of minority carriers (electrons) from the forward-biased Au/CdTe Schottky contact to the reverse-biased p -n junction (near the In/CdTe contact) through the CdTe crystal. Spectral properties of In/CdTe/Au diode detectors have also been analyzed.