A new laser method elaborated for a cone like nanostructure formation on a surface of semiconductors is reported. Diameter of the nanocone is increased gradually from top of cone till a substrate. Such structure has qualitative new properties in comparison with QWs and QDs. For example, nanocone with gradually changed diameter is gradient band gap structure [1]. Model of the nanostructures growth and optical properties of nanocones are proposed. Optical properties of elementary semiconductors such as Ge, Si and Si1-xGex solid solution after irradiation by Nd:YAG laser are investigated. Nanocones on the surface of Ge single crystal were formed by basic frequency of Nd:YAG laser radiation at intensity of 30.0 MW/cm2. This structure is characterized by patterns related to C6i point group symmetry covering all the surface of the sample and having translations symmetry. In the case of n- and p-type SiO2 /Si single crystals nanocones were formed by the second harmonic of Nd:YAG laser radiation at intensity of 2.0 MW/cm2. The same nanocones were induced on the surface of SixGe1-x/Si heterostructures with x = 0.3 and 0.4 by basic frequency of Nd:YAG laser radiation at intensities from 2.0 till 20.0MW/cm2 [2]. The same methods for formation of nanocones on a surface of compound GaAs and ternary compound Cd1-xZnxTe semiconductors were studied. Nanocones were formed on the surface of GaAs and Cd1-xZnxTe with x = 0.1 [3] by the second harmonics of Nd:YAG laser radiation at intensity within 4.0 - 12.0MW/cm2. The optical properties and surface morphology of nanostructures' formed by the laser radiation on the surface of semiconductors using Atomic force microscope, Electron scanning microscope, Photoluminescence (PL) and Raman back scattering methods were studied. Unusual photoluminescence spectrum from the irradiated surfaces was found in the visible range of spectrum. Photoluminescence from Ge, Si, SiGe/Si and GaAs nanocones can be explained by Quantum confinement effect. A shift of micro-Raman scattering spectra in Ge and GaAs is a good evidence of this suggestion. Asymmetric of photoluminescence spectra of the irradiated SiO2/Si structure is explained by Quantum confinement effect in nanocones with a gradually decrease of diameter toward the top of nanocone. The following mechanism of nanocones formation in Si1-xGex/Si structure by laser radiation is proposed: irradiation of SiGe/Si heterostructure by Nd:YAG laser initiates Ge atoms drift to the irradiated surface due to gradient of temperature - Thermogradient effect (TGE). This process is characterized by positive feedback: after every laser pulse gradient of temperature increases due to increase of Ge atoms concentration at the irradiated surface and new Ge phase formation occurs at the end of the process. Ge atoms are localized at the surface of Si like a thin film. A mismatch of Si and Ge crystal lattices leads to compressive stress of Ge layer. This stress relaxation takes place by plastic deformation of the top layer and creation of nanocones on the irradiated surface according to the modified Stransky-Krastanov' mode. The "blue shift" on 0.23mV of exciton bands in PL spectra of the irradiated Cd1-xZnxTe is explained by Exciton Quantum confinement effect in nanocones. A new PL band at 1.88 eV is found. Appearance of the PL band is explained by formation of CdTe/Cd1-xZnxTe heterostructure in the bulk of the semiconductor with x=0.18 due to TGE. For the first time was shown the possibility of 1D gradient band gap structure formation in elementary semiconductors. Thermogradient effect has a main role in initial stage of nanocones and gradient band gap structure formation by laser radiation in semiconductors. [1] Artur Medvid’,”Nano-cones Formed on a Surface of Semiconductors by Laser Radiation: Technology, Model and Properties”, in Book “Nanowires Science and Technology” edited by: Nicoleta Lupu, INTECH, Viena, pp.61-82, 2010. [2] A. Medvid', P. Onufrijevs, K. Lyutovich, M. Oehme, E. Kasper, N. Dmitruk, O. Kondratenko, I. Dmitruk, and I. Pundyk, “Self-Assembly of Nanohills in Si1-xGex/Si Hetero-Epitaxial Structure Due to Ge Redistribution Induced by Laser Radiation” J. Nanoscience & Nanotechnology, Vol.10, pp.1094-1098, 2010. [3] N.M.Litovchenko, P.M. Lytvyn, A.P. Medvid’, A.M. Mychenko, Yu.M. Naseka, O.M. Strilchuk, “Influence on the nanostructures formed by the laser scanning method on the surface of CdZnTe crystals on their low-temperature photoluminescence spectra”, Optoelectronics and semiconductor technics, Vol. 44, pp.109-113, 2009.