In-situ control of electrical properties of nanoelectromechanical resonators by electromigration for self-sustained oscillations

We use electromigration for in situ control of the electrical impedance of nanoelectromechanical resonators, the vibrations of which are detected with magnetomotive detection. The resonator consists of a doubly clamped, suspended silicon nitride beam with a gold nanowire fabricated on top. A constriction is present in the gold nanowire near the middle of the beam. As fabricated, the impedance of the device is smaller than the cable impedance of 50 Ω so that the mechanical resonance of the beam appears as a minimum on a background of the reflected ac signal in a perpendicular magnetic field. We decrease the width of the junction by inducing controlled electromigration of the gold atoms near the junction. As the electrical resistance of the nanowire is increased to near 50 Ω, the reflection background is minimized. With the vibration phase accurately measured, self-sustained oscillations of the beam resonator are excited using a phase-locked loop for a wide range of phase delay between the response and the drive. By optimizing the impedance of the nanobeam, we measure all three branches of the Duffing oscillator, including the middle one that is unstable when the driving frequency is swept without the phase-locked loop. Electromigration could serve as a versatile tool to enhance the performance of nanomechanical resonators as sensors and clocks.