Analytical study of electromechanical buckling of a micro spherical elastic film on a compliant substrate part I: Formulation and linear buckling of periodic patterns

This work presents an analytical study of the electromechanical buckling of a micro spherical thin film bonded to a compliant elastic substrate. The spherical film is subjected to electrostatic attraction forces that are induced by applying a voltage difference between an outer spherical elastic film electrode and inner rigid, fixed and grounded spherical electrode. When the applied voltage is small, the film contracts while maintaining its complete spherical shape. However, when the applied voltage reaches a critical value, the film buckles into high-ordered periodic patterns (i.e. elastic surface wrinklings). Motivated by experimental results of other studies, this work examines the critical buckling state of one-dimensional, square checkerboard and hexagonal patterns. As will be shown, the above considered patterns are associated with the same critical state, and therefore, all patterns have equal buckling voltage and critical wavelength. Furthermore, with increasing radius of the film/substrate system the electromechanical buckling response converges to the electromechanical pull-in instability of the well-known two parallel plate electrodes, as will be revealed by the asymptotic analytical solution. Finally, the elastic ripples of the electromechanically buckled film can be generated or removed by a simple On/Off switching of the applied voltage. The ability to generate and remove elastic ripples tremendously increases the potential of such microsystem to be utilized in different applications in the field of Micro and Nano electromechanical systems.