A new elaborated laser method for quantum cones formation in elementary semiconductors Si and Ge and their solid solutions is reported. A cone possesses unique properties: a small cone is a quantum dot and a long one is a quantum wire with the gradually decreasing diameter from the base till the top of the cone. Everywhere radius of cone is equal or less than Bohr' radius of electron or exciton Quantum confinement effect (QCE) takes place. Properties of quantum cones using atomic force microscope (AFM), scattering electron microscope (SEM), photoluminescence (PL) and Raman spectroscopy were studied. Unique visible PL spectrum from the surfaces with quantum cones was found and is explained by QCE. A “red” shift of Raman spectra in Ge is a good evidence of the phonon QCE in quantum cones. Asymmetry of PL spectra of the irradiated SiO2/Si structure is explained by formation graded band gap structure due to QCE in quantum cones with a graded decrease of diameter toward the top of cone. Two-stage model of quantum cones formation is proposed: Laser Redistribution of Atoms and Selective Laser Annealing. The first stage is characterized by formation of heterostructures such as Ge/Si due to drift of Ge atoms toward the irradiated surface of the sample in the gradient of temperature. New Ge phase is formed at the end of the process. Ge atoms are localized at the surface of Si like a thin film. The second stage is characterized by formation of quantum cones 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. For the first time the possibility of graded band gap 1D structure formation in elementary semiconductors was shown.