Influence of the electron density on the thickness-dependent energy gap oscillations in superconducting metallic nanofilms

The thickness-dependent energy gap oscillations in the metallic nanofilms are investigated by the use of the self-consistent numerical solutions of the Bogoliubov-de Gennes equations. It is shown, that the oscillations are induced by the quasi-particle energy quantization triggered by the confinement of electrons in the direction perpendicular to the sample. We have analyzed, how the changes in the electron density of states ($n_e$) and the electron-phonon coupling constant ($g$) influence the amplitude of the considered oscillations. It has been found, that the increase in $n_e$ and the decrease in $g$, can lead to a significant reduction of the oscillations amplitude. As a result, for the values of the mentioned parameters corresponding to some of the realistic situations the thickness-dependent superconducting gap oscillations can be almost completely suppressed.