section in a dielectric medium has been obtained in the model of free electrons and a
cylindrical potential well of finite depth. The calculations have been carried out for Au wires
in SiO 2 and in Al 2 O 3. It has been shown that a change in the geometry of the cross
section and the presence of the dielectric environment lead to a decrease in the Fermi
energy, whereas the general character of the size dependences is preserved.