Ultrahigh Frequency Nanotube Resonators

We report carbon-nanotube-based electromechanical resonators with the fundamental mode frequency over 1.3 GHz, operated in air at room temperature. A new combination of drive and detection methods allows for unprecedented measurement of both oscillation amplitude and phase and elucidates the relative mobility of static charges near the nanotube. The resonator serves as an exceptionally sensitive mass detector capable of $\sim {10}^{-18}\mathrm{g}$ resolution.

Figure 1

(a) Schematic cross section of the CNT resonator. (b) SEM image of a suspended CVD-grown carbon nanotube crossing a trench. Scale bar: 200 nm. (c) Schematic experimental diagram for the $2\omega$ method. An actuation rf signal of amplitude $\delta V_g$ at frequency $\omega$ is applied to the gate, together with a dc bias $V_g$. A carrier rf signal of amplitude $\delta V_d$ is applied to the drain at frequency $2\omega \mathrm{\text{−}}\Delta \omega$. The ac current flow through the source at the frequency $\Delta \omega$ is monitored using a lock-in amplifier with a time constant 300 ms. The lock-in reference at the frequency $\Delta \omega$ is obtained through a frequency doubler and a mixer.

Figure 2

Amplitude (in logarithmic scale) and phase of the electrical current in a vacuum $\sim {10}^{-6}\mathrm{Torr}$ (triangles) and in air (circles) for a nanobridge resonator made from coating a bare suspended CNT device with 2.5 nm indium. The data were taken at $V_g=0$, $\delta V_g=112\mathrm{mV}$, and $\delta V_d=46\mathrm{mV}$ by the $1\omega$ method.

Figure 3

Amplitude in logarithmic scale (a) and phase (b) of current response as a function of effective driving frequency $f$ for a bare CNT resonator, taken with $V_g=0$, $\delta V_g=158\mathrm{mV}$, and $\delta V_d=70\mathrm{mV}$ by the $1\omega$ method (star) and the $2\omega$ method (circle) at room temperature in a vacuum $\sim 3\times {10}^{-6}\mathrm{Torr}$. The solid lines (gray) in (a) and (b) are the fitting results according to the theory described in the text, with $Q=15$, ${\omega }_0/2\pi =382.7\mathrm{MHz}$, and ${\varphi }_b=-92.25°$. [Experimentally, the cable length difference of the reference and the input of the lock-in induced a linearly varying phase with respect to frequency ($\sim 0.99°/\mathrm{MHz}$), which was added to the total phase $\varphi$ in Eq. (1) in the fitting.] The derivative of phase with respect to the effective driving frequency $d\varphi /df$ for the fitted data is shown in (c).

Figure 4

Electrical response (with amplitude in logarithmic scale) of a Fe-coated nanobridge resonator (circle) and the same device after an additional loading of 2 nm Fe (triangle), measured with $V_g=0$ and $\delta V_g=21\mathrm{mV}$ by the $1\omega$ method.