Thickness Effect on Fluctuation of Electron States in Thin Film and Implication to Lattice Constant Change Due to Size Reduction

We propose a model for predicting the fluctuations of electron states in thin films as function of film thickness. The model was derived based on the assumption of the existence of potential barrier fluctuations on the film surface. Since the wave functions of electrons in the film is determined by the boundary conditions of potential on the film surface, potential fluctuations on the film surface implies the fluctuations of electron states in the film. The model was then extended to predict the effect of size on the lattice constant of thin films or nanoparticles. The derived equations can explain fairly several experimental data.