On the basis of analysis of experimental results, a two-stage mechanism of nanocones formation on the irradiated surface of semiconductors by Nd:YAG laser is proposed for elementary semiconductors and solid solutions such as: Si, Ge, SiGe and CdZnTe. Properties observed are explained in the frame of Quantum confinement effect. The first stage of the mechanism is characterized by formation of a thin strained top layer, due to redistribution of point defects in temperature gradient field induced by laser radiation. The second stage is characterized by mechanical plastic deformation of the stained top layer leading to arising of nanocones, due to selective laser absorption of the top layer. The nanocones formed on the irradiated surface of semiconductors by Nd:YAG laser possessing the properties of 1D graded band gap has been found for Si, Ge and SiGe as well, however QD structure in CdTe was observed . The model is confirmed by "blue shift" of bands in photoluminescence spectrum, "red shift" of longitudinal optimal line in Raman back scattering spectrum of Ge crystal, appearance of Ge phase in SiGe solid solution after irradiation by the laser at intensity 20 MW/cm2 and non-monotonous dependence of Si crystal micro-hardness as function of the laser intensity.