Electric field localizations in thin dielectric films with thickness non-uniformities

Thickness non-uniformities in electrostatic capacitors and in electroactive polymers – arising from manufacturing processes or electromechanical induced inhomogeneous deformations – may lead to drastic charge and electric field localizations and, ultimately, to an anticipated device failure. Based on a geometric interpretation of the Gauss equation enlightening the effect of the electrode curvature, we obtain an analytic expression of the electric field and of the surface charge density localization for non perfectly planar capacitors with symmetric thickness non-uniformities. The efficiency of the model is exploited by analyzing specific boundary value problems of technological interest.

► We get an approximate expression of the electric field in thin undulated capacitors.
► We enlighten the role of planarity imperfections in charge localization effects.
► We make use of a geometrical interpretation of the Gauss equation.
► Physically realistic examples illustrate the accuracy of the results.