Image potential near a gradual interface between two dielectrics

Abstract

The image potential is calculated near a model interface in which the dielectric constant changes continuously in a thin transition layer between two dielectrics. If the transition is sufficiently smooth, the image potential is bounded and continuous, as opposed to the divergent and discontinuous $\frac{1}{z}$ dependence for an abrupt interface at $z=0\mathrm{}$. Results of model calculations of the image potential for the Si-Si${\mathrm{O}}_2$ and liquid-helium-vacuum interfaces are presented. Application of the model to the calculation of energy levels of electrons on liquid helium gives good agreement with the experimental results of Grimes et al. when an effective thickness of 0.57 nm is used for the helium-vacuum transition layer.