Amro M. Elshurafa, et al., "Low-voltage puzzle-like fractal microelectromechanial system variable capacitor suppressing pull-in" Micro & Nano Letters 7, (9), 2012, 965.
Abstract: This Letter introduces an electrostatically actuated fractal MEMS variable capacitor that, by utilising the substrate, extends the tuning range (TR) beyond the theoretical limit of 1.5 as dictated by the pull-in phenomenon. The backbone concept behind the fractal varactor is to create a suspended movable plate possessing a specific fractal geometry, and to simultaneously create a bottom fixed plate complementary in shape to the top plate. Thus, when the top plate is actuated, it moves towards the bottom plate and fills the void present within the bottom plate without touching it akin to how puzzle pieces are assembled. Further, a reasonable horizontal separation is maintained between both the plates to avoid shorting. The electrostatic forces come from the capacitance formed between the top plate and bottom plate, and from the capacitance formed between the top plate and the doped substrate. The variable capacitor was fabricated in the PolyMUMPS process and provided a TR of 4.1 at 6 V, and its resonant frequency was in excess of 40 GHz.