Electrostatic image force energy for charges in three-layer structures: exact formulas and their approximations

Abstract

Abstract The problem of image force energy W(Z) in three-layer plane structures, where Z is the coordinate perpendicular to the layers, has been reconsidered. In the classical electrostatic limit, where the dielectric permittivities ɛ i of all structure components (i = 1, 2, 3) are constants, the exact general dependences W(Z) were obtained for each layer and any ɛ i -combination in terms of the Lerch transcendent function. For certain combinations of ɛ i , an ion adsorption minimum was found to arise in one of the covers far from the interlayer. Some other combinations of ɛ i can lead to the appearance of a potential barrier, which does not permit a free charge existing in the cover to approach the interlayer, although it will be attracted to the interlayer in the close vicinity of the latter. For symmetric structures (ɛ 1 = ɛ 3), the asymptotic behavior of W ( Z → ∞ ) was shown to be Z − 2 rather than Z − 1 , as it takes place in the two-layer case. Simple approximate analytical formulas that describe W(Z) and possess high accuracy for arbitrary relationships among the ɛ i -constants were proposed.