Mechanical Detection of Carbon Nanotube Resonator Vibrations

Bending-mode vibrations of carbon nanotube resonators were mechanically detected in air at atmospheric pressure by means of a novel scanning force microscopy method. The fundamental and higher order bending eigenmodes were imaged at up to 3.1 GHz with subnanometer resolution in vibration amplitude. The resonance frequency and the eigenmode shape of multiwall nanotubes are consistent with the elastic beam theory for a doubly clamped beam. For single-wall nanotubes, however, resonance frequencies are significantly shifted, which is attributed to fabrication generating, for example, slack. The effect of slack is studied by pulling down the tube with the tip, which drastically reduces the resonance frequency.

Figure 1

(a) SEM image and schematic of the nanotube resonator device. The motion is actuated with a side gate ($G$) that is typically $0.3–1\mu \mathrm{m}$ from the tube. (b) Motion of the nanotube as a function of time. A high-frequency term at $f_{\mathrm{RF}}$ is used to match the resonance frequency of the nanotube, and the high-frequency oscillation is modulated at $f_{\mathrm{mod}}$. (c) Experimental setup.

Figure 2

(a) Topography and (b) vibration images for a 770 nm long MWNT resonator. Images are $0.5\times 1\mu {\mathrm{m}}^2$. The vibration images have been low-pass filtered with identical parameters for the 3 images. $V_G^{\mathrm{dc}}=-2.5\mathrm{V}$. $V_G^{\mathrm{ac}}$ is 1 V in (b),(c) and 1.5 V in (d). (e) Detected displacement from (b)–(d). The signal of the third eigenmode has been divided by 1.5 to account for the different $V_G^{\mathrm{ac}}$’s. (f) Calculated displacement. $Q_1=5$, $Q_2=11$, and $Q_3=16$. $x_1=52\mathrm{nm}$ and $x_2=295\mathrm{nm}$. (g) Resonance peak of the fundamental eigenmode for a 265 nm long MWNT resonator. $V_G^{\mathrm{ac}}=1.5\mathrm{V}$ and $V_G^{\mathrm{dc}}=3\mathrm{V}$.

Figure 3

(a) Topography and vibration images of a 572 nm long SWNT at 290 MHz without any image filtering. $V_G^{\mathrm{ac}}=0.7\mathrm{V}$ and $V_G^{\mathrm{dc}}=5\mathrm{V}$. (b) Resonance frequency as a function of slack.