Quantum-well states in a thin Ag film on a Ni(111) substrate

The spectrum of quantum-well states is studied in an Ag film during its deposition on a Ni(111) substrate from thicknesses of a submonolayer to 14 monolayers. The dependence of the quantum-state energies on the film thickness is analyzed using different theoretical models: the simplest model of a potential well between infinite walls; a model of a potential well between finite barriers; and a model of phase accumulation during reflections of an electron wave within different approximations. It is demonstrated that the agreement between the experimental data and theoretical estimations improves as one goes from the crude model of a potential well between infinite walls to the model of a potential well between finite barriers and then to the classical phase accumulation model. The best description of the energy spectrum of quantum-well states can be achieved using an extended phase accumulation model that takes into account scattering of electron waves on the film-substrate boundary including the scattering that occurs outside the band gap of the substrate electronic structure.