Self-compressed inhomogeneous stabilized jellium model and surface relaxation of simple metal thin films
The interlayer spacings near the surface of a crystal are different from that of the bulk. As a result, the value of the ionic density in the normal direction and near to the surface shows some oscillations around the bulk value. To describe this behavior in a simple way, we have formulated the self-compressed inhomogeneous stabilized jellium model and have applied it to simple metal thin films. In this model, for a $\nu$-layered slab, each ionic layer is replaced by a jellium slice of constant density. The equilibrium densities of the slices can be determined by minimizing the total energy per electron of the slab with respect to the slice densities. To avoid the complications that arise due to the number of independent slice-density parameters for large-$\nu$ slabs, we consider a simplified version of the model with three jellium slices: one inner bulk slice with density $\bar n_1$ and two similar surface slices of densities $\bar n_2$. In this simplified model, each slice may contain more than one ionic layer. Application of this model to the $\nu$-layered slabs ($3\le\nu\le 10$) of Al, Na, and Cs shows that, in the equilibrium state, $\bar n_1$ and $\bar n_2$ assume different values, which is significant in the Al case, and the state is more stable than that predicted in the homogeneous model in which only one global jellium density is used for the whole system. In addition, we have calculated the overall relaxations, the work functions, and the surface energies, and compared with the results of the earlier works.