Theoretical and experimental study of the bending influence on the capacitance of interdigitated micro-electrodes patterned on flexible substrates

Interdigitated electrodes are common structures in the fields of microelectronics and MEMS. Recent developments in flexible electronics compel an understanding of such structures under bending constraints. In this work, the behavior of interdigitated micro-electrodes when subjected to circular bending has been theoretically and experimentally studied through changes in capacitance. An analytical model has been developed to calculate the expected variation in capacitance of such structures while undergoing outward and inward bending along the direction perpendicular to the electrodes. The model combines conformal mapping techniques to account for the electric field redistribution and fundamental aspects of solid mechanics in order to define the geometrical deformation of the electrodes while bending. To experimentally verify our theoretical predictions, several interdigitated electrode structures with different geometries were fabricated on polymeric substrates by means of photolithography. The samples, placed in a customized bending setup, were bent to controlled radii of curvature while measuring their capacitance. A maximum variation in capacitance of less than 3% was observed at a minimum radius of curvature of 2.5mm for all the devices tested with very thin electrodes whereas changes of up to 7% were found on stiffer, plated electrodes. Larger or smaller variations would be possible, in theory, by adjusting the geometry of the device. This work establishes a useful predictive tool for the design and evaluation of truly flexible/bendable electronics consisting of interdigitated structures, allowing one to tune the bending influence on the capacitance value through geometrical design. (c) 2013 AIP Publishing LLC.