Tuning of Nanotube Mechanical Resonances by Electric Field Pulling

We show here that field emission (FE) can be used to directly observe the vibration resonances ${\nu }_R$ of carbon nanotubes (CNTs) and that the tension created by the applied field allows the tuning of these resonances by up to a factor of 10. The resonances are observable by the changes they create in the FE pattern or the emitted FE current. The tuning is shown to be linear in voltage and to follow from the basic physics of stretched strings. The method allows one to study the mechanical properties of individual multiwall carbon nanotubes within an ensemble and follow their evolution as the CNTs are modified. The tuning and detection should be useful for nanometric resonant devices.

Figure 1

Schema of the experimental field emission setup used to measure the resonances (distances: tip anode $\sim 2\mathrm{m}\mathrm{m}$, tip screen $\sim 3\mathrm{c}\mathrm{m}$, and screen size $\sim 4\mathrm{c}\mathrm{m}$).

Figure 2

$V_A=700\mathrm{V}$. (a) FEM pattern out of resonance. The pattern from NT1 is overexposed so that those of NT2 and NT3 are visible. The 4 cm microchannel plate (mcp) fills most of the image. (b) NT1 in vertical resonance, $m=2$ (see below), $\nu =0.9588\mathrm{M}\mathrm{H}\mathrm{z}$. (c) NT1 in horizontal resonance, $m=1$, $\nu =0.7399\mathrm{M}\mathrm{H}\mathrm{z}$. (d) NT2 in resonance, $\nu =0.6017\mathrm{M}\mathrm{H}\mathrm{z}$. (e) NT3 in resonance, $\nu =1.0463\mathrm{M}\mathrm{H}\mathrm{z}$. (f) Total FE current $I_{\mathrm{F}\mathrm{E}}(\nu )$ as NT1 is scanned through resonance.

Figure 3

Dependence of a selection of ${\nu }_R$’s on $V_A$ for NT1 and NT2. Only one measure by FIM for NT(1,1) is shown though four series corresponding to modes (1,1) to (4,1) were measured. We find ${\nu }_{R0}\simeq 190\mathrm{k}\mathrm{H}\mathrm{z}$ and $p\simeq 0.91\mathrm{k}\mathrm{H}\mathrm{z}/\mathrm{V}$ for NT1(1,1) FEM, and ${\nu }_{R0}\simeq 280\mathrm{k}\mathrm{H}\mathrm{z}$ and $p\simeq 1.01\mathrm{k}\mathrm{H}\mathrm{z}/\mathrm{V}$ for NT1(1,1) FIM. They also displayed the same polarization, thus establishing the correspondence between the two series.