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. The observed properties are explained in the frame of Quantum confinement effect. 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, such as: Si, Ge and their solid solution SiGe. The first stage - Laser Redistribution of Atoms (LRA) is characterized by formation of hetero-structures such as: Ge/Si due to drift of Ge atoms toward the irradiated surface of the sample in the gradient of temperature, the so-called Thermogradient effect [1]. This process is characterized by positive feedback: after every laser pulse, the gradient of temperature increases due to increase of Ge atoms’ concentration at the irradiated surface. New Ge phase is formed at the end of the process. Ge atoms are localized at the surface of Si like a thin film. As a result, LRA stage gradually transits to Selective Laser Annealing (SLA) stage. The second stage, SLA, is characterized by formation of nanocones on the irradiated surface of a semiconductor by selective laser heating of the top layer with following mechanical plastic deformation of the layer as a result of relaxation of the mechanical compressive stress arising between these layers due to mismatch of their crystal lattices and selective laser heating. SLA occurs due to higher absorption of the laser radiation by the top layer than the buried layer. The proposed model is confirmed by “blue shift” bands in photoluminescence spectrum, “red shift” of LO line in Raman back scattering spectrum of Ge crystal and non-monotonous dependence of Si crystal micro-hardness as function of the laser intensity.