In this work we study the mechanisms of laser radiation interaction with elementary semiconductors such as Si and Ge and their solid solution SiGe. As a result of this investigation, the mechanisms of nanocones and microcones formation on a surface of semiconductor were proposed. We have shown the possibility to control the size and the shape of cones both by the laser. The main reason for the formation of nanocones is the mechanical compressive stresses due to the atoms' redistribution caused by the gradient of temperature induced by strongly absorbed laser radiation. According to our investigation, the nanocone formation mechanism in semiconductors is characterized by two stages. The first stage is characterized by formation of a p-n junction for elementary semiconductors or of a Ge/Si heterojunction for SiGe solid solution. The generation and redistribution of intrinsic point defects in elementary semiconductors and Ge atoms concentration on the irradiated surface of SiGe solid solution in temperature gradient field take place at this stage due to the thermogradient effect which is caused by strongly absorbed laser radiation. The second stage is characterized by formation of nanocones due to mechanical plastic deformation of the compressed Ge layer on Si. Moreover, a new 1D-graded band gap structure in elementary semiconductors due to quantum confinement effect was formed. For the formation of microcones Ni/Si structure was used. The mechanism of the formation of microcones is characterized by two stages as well. The first stage is the melting of Ni film after irradiation by laser beam and formation of Ni islands due to surface tension force. The second step is the melting of Ni and subsequent manifestations of Marangoni effect with the growth of microcones.