Clamping instability and van der Waals forces in carbon nanotube mechanical resonators.

We investigate the role of weak clamping forces, typically assumed to be infinite, in carbon nanotube mechanical resonators. Due to these forces, we observe a hysteretic clamping and unclamping of the nanotube device that results in a discrete drop in the mechanical resonance frequency on the order of 5-20 MHz, when the temperature is cycled between 340 and 375 K. This instability in the resonant frequency results from the nanotube unpinning from the electrode/trench sidewall where it is bound weakly by van der Waals forces. Interestingly, this unpinning does not affect the Q-factor of the resonance, since the clamping is still governed by van der Waals forces above and below the unpinning. For a 1 µm device, the drop observed in resonance frequency corresponds to a change in nanotube length of approximately 50-65 nm. On the basis of these findings, we introduce a new model, which includes a finite tension around zero gate voltage due to van der Waals forces and shows better agreement with the experimental data than the perfect clamping model. From the gate dependence of the mechanical resonance frequency, we extract the van der Waals clamping force to be 1.8 pN. The mechanical resonance frequency exhibits a striking temperature dependence below 200 K attributed to a temperature-dependent slack arising from the competition between the van der Waals force and the thermal fluctuations in the suspended nanotube.