The In/CdTe/Au p-n junction-diode X/γ-ray detectors, formed by frontside laser irradiation doping, were studied using I-V characteristics, measured at different temperatures, and spectra of 241 Am, 57 Cs, and 137 Cs isotopes, obtained in a wide bias range V = 60-380 V. A key feature of the technology was low-temperature ( ~90 ºC) vacuum annealing of polished in a Br-methanol solution detector-grade (111) oriented p-like CdTe crystals prior to the deposition of an In dopant film and formation of electrodes. After laser-induced doping of a layer near the In/CdTe interface and deposition of an Au electrode (ohmic contact), the In/CdTe/Au structures showed high rectification. The I-V measurements and calculations revealed that the dominant charge transport mechanism at low reverse bias was generation-recombination in the space charge region. It was noteworthy that the reverse current linearly increased at higher V ≥ 50 V when the depletion region extended over the entire crystal thickness. A sharp increase in I at higher V, that was inherent in diode structures (I ~ V n , n > 1), was not observed that evidenced a perfect ohmic contact, i.e. no injection of minority carriers from the Au/CdTe contact occurred. The detectors formed on the preliminary annealed CdTe crystals showed high energy resolution ((FWHM = 0.99 %@662keV at V = 300 V). Furthermore, high spectroscopic characteristics (detection efficiency, energy resolution, true energy position of the 662 keV peak) were observed (with a deviation < 20 %) at V =150-400V.