Quality-Factor Enhancement of Nanoelectromechanical Systems by Capacitive Driving Beyond Resonance

Nanoelectromechanical systems are considered as ultrasensitive devices for mass and force detection. Capacitive actuation is widely used in these devices but is known to degrade the quality factor of the resonator due to dc electrostatic damping. We report the enhancement of the quality factor of SiC vibrating nanowires detected nano-optomechanically and electrically by applying an ac capacitive driving at a frequency above both the resonance frequency and the electrical cutoff frequency. Self-oscillations are demonstrated for optimal conditions. We develop an analytical model of the phenomenon and show that it can lead to an improvement of the force sensitivity.

Figure 1

(a) Schematic of a vibrating SiC nanowire on a tungsten tip submitted to an ac voltage $V_{\mathrm{ac}}$ or a dc voltage $V_{\mathrm{dc}}$. (b) SEM image of the silicon carbide nanowire NW2 close to a gold counter electrode for $V_{\mathrm{ac}}=V_{\mathrm{dc}}=0\mathrm{V}$. (c) SEM image of NW2 in self-oscillation for $V_{\mathrm{ac}}=19\mathrm{V}$, $V_{\mathrm{dc}}=0\mathrm{V}$, and a driving frequency $\mathrm{\Omega }/2\pi =810\mathrm{kHz}$ well above the resonance frequency of 40 kHz.

Figure 2

(a) Evolution of the displacement noise spectrum of NW1 as a function of the driving frequency $\mathrm{\Omega }/2\pi$ for $V_{\mathrm{ac}}=10\mathrm{V}$ and $V_{\mathrm{dc}}=0\mathrm{V}$. (b) Evolution of the quality factor $Q$ as a function of the driving frequency. The solid line is a fit of the quality factor with Eq. (4). The dashed line is the quality factor without an ac voltage.

Figure 3

(a) Schematic of the mechanism involved in the quality-factor enhancement induced by an ac voltage. $F_{\mathrm{ext}}$ is an external force like the thermal-noise force. $F_{\mathrm{tot}}$ is the sum of the external force and the two feedback forces. $\chi (\omega )$ is the mechanical susceptibility of the nanowire. $H(\omega )e^{i\phi }$ is the transfer function of the transmission line. $U_0$ and $U_1$ are calculated in Ref. [26]. The two crossed circles represent signal mixers responsible for the nonlinear effects and originating from the $C^{\prime }$ terms. (b) Evolution of the term ${\Re }^{\mathrm{\Omega }}$ as a function of the driving frequency with the experimental parameters of NW1. The smaller the black arrow, the smaller the effect on the damping. (c) Evolution of the term ${\Im }^{\mathrm{\Omega }}$ as a function of the driving frequency with the experimental parameters of NW1. The damping is reduced as long as the blue arrow is longer than the red arrow.

Figure 4

(a) Evolution of the displacement noise spectrum of NW1 after annealing as a function of the driving frequency $\mathrm{\Omega }/2\pi$ for $V_{\mathrm{ac}}=10\mathrm{V}$ and $V_{\mathrm{dc}}=0\mathrm{V}$. Satellite peaks related to self-oscillation appear between 650 and 850 kHz. (b) Evolution of ${\omega }_0/{\mathrm{\Gamma }}_{\mathrm{ac}}$ (which corresponds to the quality factor $Q$ outside the self-oscillation region) as a function of the driving frequency after annealing. The solid line is a fit of the quality factor with Eq. (4). The dashed line is the quality factor without an ac voltage. (c) Evolution of the vibration amplitude at resonance as a function of the driving frequency.