Energies and fermi level of electrons in thin size‐quantized metal films

The energies and the Fermi levels of electrons in thin size‐quantized metal films are investigated. Frequently a model with a constant potential is used and it is demanded that the wave functions or their derivatives vanish on planes parallel to the film surfaces. The position of these planes relative to the ion lattice is determined from the condition that the Fermi energy does not include a term inversely proportional to the film thickness. A comparison with numerical results of a fully self‐consistent calculation reveals that the results for the case that the wave functions vanish on the bounding planes (Dirichlet boundary conditions) form a satisfactory approximation.