5.4.1 Electromechanical OscillatorsAn electromechanical oscillator based on a nanotube has been experimentally demonstrated in Ref. [26]. The device consists of a three terminal transistortype device with a nanotube forming the channel (Fig. 5.15). The nanotube is suspended over a trench between the source and drain, and is capacitively coupled to the gate terminal. Applying an oscillating gate voltage causes the nanotube to mechanically oscillate. When the applied ac frequency matches the resonant frequency of the nanotube, the amplitude of mechanical oscillation becomes large. The coupling between the nanotube displacements and the gate electrostatics arises because a change in the distance between the nanotube and the gate causes a change in the capacitance between the nanotube and gate. For gate-controlled electronic devices, the charge on the carbon nanotube is proportional to the gate voltage: n = CgVg where Cg is the gate capacitance. This charge is attracted to the image charge of opposite sign on the gate. The force can be written as (5.31)where z is the distance between the nanotube and the gate and z0 is the equilibrium nanotube position. The applied gate potential is of the form(5.32)and consists of a background DC component over which small time-dependent oscillations of frequency are superposed. The electrostatic force on the nanotube is then given by(5.33)Where . The force on the nanotube thus consists of a static component that can be used to tune the tension and an oscillating component to probe the nanotube resonance. In addition to the electrostatic force, the nanotube experiences an elastic force that tends to bring it back to its equilibrium shape, and is of the form