The investigation of surface morphology using atomic force microscope has shown self-organizing of the nanocones on the surface of CdZnTe crystal after irradiation by strongly absorbed Nd:YAG laser irradiation at an intensity of 12.0 MW/cm2. The formation of nanocones is explained by the presence of a thermogradient effect in the semiconductor. The appearance of a new exciton band has been observed after irradiation by the laser which is explained by the exciton quantum confinement effect in nanocones.