Ming Hsieh Department of Electrical Engineering, †Department of Physics and Astronomy and ‡Department of Materials Science, University of Southern California , Los Angeles, California 90089, United States.
Nano Lett. 2014 May 14;14(5):2426-30. doi: 10.1021/nl500096p. Epub 2014 Apr 23.
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.
我们研究了弱夹持力（通常假定为无穷大）在碳纳米管机械谐振器中的作用。由于这些力的存在，我们观察到纳米管器件的滞后夹持和解夹，导致机械共振频率离散下降约 5-20MHz，当温度在 340 到 375K 之间循环时。这种共振频率的不稳定性是由于纳米管从电极/沟槽侧壁上解钉，在那里它被范德华力弱束缚。有趣的是，这种解钉不会影响共振的 Q 因子，因为在解钉上方和下方，仍然由范德华力来控制夹持。对于 1μm 的器件，观察到的共振频率下降对应于纳米管长度的变化约为 50-65nm。基于这些发现，我们引入了一个新模型，该模型包括由于范德华力导致的零栅压附近的有限张力，并且与实验数据的吻合度优于完美夹持模型。从机械共振频率对栅极的依赖性中，我们提取出范德华夹持力为 1.8pN。机械共振频率在 200K 以下表现出显著的温度依赖性，这归因于由于范德华力和悬浮纳米管中的热涨落之间的竞争而产生的温度相关的松弛。
