Thickness dependence of the work function in case of ultra-thin metallic layers

Abstract The precise, analytical equation for calculating the work function presented by authors in their earlier articles enables the theoretical analysis of phenomena occurring on the surface of the metal in the case when its dimensions are reduced to the nanoscale. The oscillations of the work function observed in these conditions result directly from reduction of the physical dimension analyzed sample, because the Fourier transform of the electron density n restricted to closed interval becomes an oscillatory function. The numerical calculations carried out on the example of sodium and titanium allow to observe changes in the work function of both metals depending on the layer thickness in wide range. In order to compare the obtained results with the experimental data, additional numerical calculations for Pb were performed (chapter 4).