Nanocones’ formation on a surface of CdxZn1-xTe solid solution with x=0.1 after irradiation by strongly absorbed Nd:YAG laser radiation (LR) with intensity I=10.0 MW/cm2 was observed. Studying the nanocones’ optical properties using the low temperature 50K photoluminescence (PL) method, a new exciton band at energy up to 1.872 eV and at the same time, shift of A0X and D0X exciton bands on 2.5 meV toward the higher energy of quantum, the so-called “blue shift”, for the first time were observed. Appearance of a new PL band and the “blue shift” of the exciton bands are explained by Exciton quantum confinement (EQC) effect in nanocones and by mechanical compressive stress of CdTe top layer formed on the irradiated surface of the solid solution, correspondingly. This process takes place in the following way: irradiation of the CdxZn1-xTe solid solution by the laser leads to the drift of Cd atoms toward irradiated surface and of Zn atoms - in the bulk of the semiconductor due to high gradient of temperature, the so-called Termogradient effect (TGE) [1]. As a result, formation of CdTe/CdxZn1-xTe hetero-structure takes place due to replacement of Zn atoms by Cd atoms at the irradiated surface. The opposite process takes place under the top layer of the semiconductor – Zn atoms replace Cd atoms. As the result of this redistribution the “red shift” of PL spectrum has been observed [2] at low intensity of LR, lower than 4.0 MW/cm2. The “red shift” of PL spectrum takes place because the band gap of CdTe is narrower than the band gap of CdZnTe solid solution with any concentration of Zn atoms. At higher intensity of LR the TGE leads to “blue shift” of the A0X exciton band on maximum shift 3.1 meV in PL spectrum at intensity of the laser 8.1 MW/cm2. The top layer of CdTe/CdxZn1-xTe hetero-structure, it means CdTe, is exposed to mechanical compressive stress due to mismatch of CdTe and CdxZn1-xTe crystalline lattice. The next laser pulses anneal the structure and lead to relaxation of mechanical compressive stress in the top layer. This comes to expression as self-assembly of nanocones on the irradiated surface of the structure. Appearance of the nanocones leads to the rise of a new band in PL spectrum of the structure and to the decrease of A0X and D0X exciton bands’ “blue shift” in PL spectrum. Reconstruction of this band shows that it consists of three lines which look like A0X, D0X and A0X–LO lines (the distance between the lines and their width FWHM are the same) in the non-irradiated PL spectrum of the semiconductor. Therefore, we connect the appearance of both the new band in PL spectrum and the nanocones’ formation on the irradiated surface of the semiconductor with EQC in nanocones and denote them as A0XQC and D0XQC lines. Calculation of quantum dot diameter using formula from paper [3] and the shift of PL spectrum on 0.23 eV give diameter of the quantum dots up to 10.0 nm. These data correspond to the size of nanocones: height and diameter of the bottom of the cones are 10.0 nm, measured using 3D image of AFM.