A technique for synthesizing nanostructures by current lithography in a scanning tunneling microscope (STM lithography) in layered Au/Si structures has been developed. An experimental dependence of the geometric dimensions of the created nanostructures on the time of current STM lithography has been obtained. A theoretical model for the growth of nanostructures is proposed, which explains the nonlinear dependence of the radius of the obtained nanostructures on time with saturation in the region of large radii. Keywords: Au/Si nanostructures, STM lithography, growth rate, modeling.