Dimensionally hybrid electric potentials and fields in high-permittivity thin films and interfaces

An analytic model for electric and exchange interactions of probe charges in high-permittivity thin films yields a dimensionally hybrid electrostatic potential which interpolates between the two-dimensional logarithmic potential at short distances and the three-dimensional r−1 potential for large distances. A comparison with the solution from image charges indicates that the analytic model is a very good approximation for distances r≥a, where 2a is the thickness of the dielectric film.