In this work, we study the mechanism of nanocone formation on a surface of elementary semiconductors by Nd:YAG laser radiation. Our previous investigations of SiGe and CdZnTe solid solutions have shown that nanocone formation mechanism is characterized by two stages. The first stage is characterized by formation of heterostructure, for example, Ge/Si heterostructure from SiGe solid solutions, and the second stage is characterized by formation of nanocones by mechanical plastic deformation of the compressed Ge layer on Si due to mismatch of Si and Ge crystalline lattices. The mechanism of nanocone formation for elementary semiconductors is not clear until now. Therefore, the main goal of our investigations is to study the stages of nanocone formation in elementary semiconductors. A new mechanism of p-n junction formation by laser radiation in the elementary semiconductor as a first stage of nanocone formation is proposed. We explain this effect by the following way: p-n junction is formed by generation and redistribution of intrinsic point defects in temperature gradient field - the thermogradient effect, which is caused by strongly absorbed laser radiation. According to the thermogradient effect, interstitial atoms drift towards the irradiated surface, but vacancies drift to the opposite direction - in the bulk of semiconductor. Since interstitials in Ge crystal are of n-type and vacancies are known to be of p-type, a n-p junction is formed. The mechanism is confirmed by the appearance of diode-like current-voltage characteristics after i-Ge irradiation crystal by laser radiation. The mechanism in Si is confirmed by conductivity type inversion and increased microhardness of Si crystal. The second stage of nanocone formation is laser heating up of top layer enriched by interstitial atoms with its further plastic deformation due to compressive stress caused by interstitials in the top layer and vacancies in the buried layer.