This paper proposes, for the first time, the investigation of the SG-FET small slope switch based on a hybrid numerical simulation approach combining ANSYS (TM) Multiphysics and ISE-DESSIS (TM) in a self-consistent system. The proposed hybrid numerical simulations uniquely enables the investigation of the physics of complex Micro-Electro-Mechanical/solid-state devices, such as SG-FET. Abrupt switching and effect of gate charges are demonstrated. The numerical data serves to calibrate an analytical EKV-based SG-FET model, which is the used to design and originally simulate a sub-micron (90nm) scaled SG-FET complementary inverter. It is demonstrated that, due to abrupt switch in the subthreshold region and electro-mechanical hysteresis, the SG-FET inverter provides significant power saving (1-2 decades reduction of inverter peak current and practically, no leakage power) compared with traditional CMOS inverter.