Analytical model of oscillating size dependence of energy and force characteristics of subatomic metal films

For a wide thin film of thickness L, the expansion of energy characteristics in powers of 1/L is constructed using the free-electron approximation and a model of a potential well of finite depth. The errors in each order of the expansion are analyzed. Using the exact formulas, the thickness dependences of the work function and of the electronic contribution to the elastic force for Al, Au, Ag, and Na films are calculated. It is concluded that the work function of a low-dimensional metal structure is always smaller than that of the corresponding semi-infinite metal.