“…In micro-electro-mechanical systems (MEMS) devices, such as switch (Naito et al 2010), variable capacitor (BakriKassem and Mansour 2004), resonator (Elshurafa et al 2011), micro mirror (Amaya et al 2011;Kim et al 2009), gyroscope (Guo et al 2010), microtweezer (Harouche and Shafai 2005) microscanner (Ataman and Urey 2006), interferometer (Lee et al 2011), attenuator (Yeh et al 2006), energy harvester , force sensor (Rajagopalan and Saif 2011), etc., electrostatic capacitors are mostly used components, which are contained of movable mechanical structures for electrostatic actuation or capacitive sensing (Amaya et al 2009;Elata and Leus 2005;Tilleman 2004;Carlen et al 2005;Sun et al 2002;Eswaran and Malarvizhi 2012;Zhang and Fang 2009). Accurate estimation of electrostatic forces or driven voltages on the MEMS structures is very important for efficient design and performance even subsequent use of the electrostatically driving devices (Jaecklin et al 1992;Chen and Miao 2007;Kang et al 2009;Harness and Syms 2000;Beyeler et al 2009).…”