  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.
