Self-detecting gate-tunable nanotube paddle resonators

Abstract

We have fabricated suspended metal paddle resonators with carbon nanotubes functioning as self-detecting torsional springs. We observe gate-tunable resonances that either tune to higher or to lower frequencies when increasing the dc voltage on the back gate. We attribute the former modes to flexural vibrations of the paddle resonator, while the latter ones are identified as torsional vibrations. Compared to top-down silicon fabricated paddle resonators, nanotube springs have smaller torsional spring constants and provide a larger frequency tunability. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2985859͔Mechanical resonators made from carbon nanotube ͑CNT͒ components show great promise in nanoelectromechanical systems. Due to their small radii, a deflection of only a few nanometers induces strain ͑tension͒ that significantly changes the properties of the resonators. 1,2 Nanotubes are furthermore ideal as building blocks for resonators due to their electronic properties, which can be modified by uniaxial or torsional strain 3-5 or by a gate-induced charge. 1,2 Recently, paddle resonators with nanotube springs have been fabricated and measured using transmission electron or optical microscopy. [6][7][8] The small nanotube radii in these devices, lead to very small torsional spring constants ͑10 −15 -10 −18 Nm/ rad͒ so that they are easily twisted, 4,6 which makes them ideal for sensing applications. A paddle resonator is expected to have mechanical vibration modes with both flexural and/or torsional components. In this letter, we present the first measurements on the dynamic behavior of paddle resonators with self-detecting nanotube springs and show that torsional and flexural modes can be distinguished based on their gate tunability. This identification may lead to mode specific sensor applications.Devices ͓schematics of the device are shown in Fig. 1͑a͔͒ are made on a highly p ++ doped silicon wafer with 1 m silicon oxide layer on top. The doped silicon is used as a back-gate electrode to actuate the paddle resonators electrostatically. Nanotubes are grown by means of chemical vapor deposition 9 and located with respect to predefined reference markers. Source and drain electrodes ͑5 nm chromium and 50 nm gold͒ are defined with e-beam lithography, followed by a separate lithography step to define the metal paddles ͑10 nm chromium and 5 -10 nm gold͒ on top of the nanotube. The samples are annealed at 400°C in argon to improve the adhesion of the paddle to the nanotube. To suspend the devices, an etch mask is defined by e-beam lithography, followed by a wet-etch with a buffered HF solution. A scanning electron micrography image of a typical paddle resonator is shown in Fig. 1͑b͒.The devices are mounted onto a custom made printed circuit board with an on-chip bias-T and 50 ⍀ terminator. The mounted sample is placed into a vacuum chamber, which is pumped down to a pressure of 10 −5 mbar. The paddle resonator is electrostatically actuated with an amplitude modulated ͑AM͒ voltage V g ac ͑100% modulation, carr...

Mechanical systems in the quantum regime

“…Subsequently Witkamp et al [20] identified the bending mode vibrations of a carbon nanotube. Nowadays the technique has been employed by many groups, not only restricted to carbon nanotubes [76,78,126,82,83,85], but also applied to suspended graphene sheets [103,104], free-hanging semiconducting nanowires [94,96] and charge-density-wave sheets [105]. Furthermore, several variations to the original mixing scheme have been implemented, including FM [85] and AM modulation [126].…”

“…Refs. [125,126,57]), thermal effects [127,122], and electromagnetic (optical) properties [55,62,128].…”

Carbon Nanotubes as Ultrahigh Quality Factor Mechanical Resonators

“…High Q-values combined with high resonance frequencies are an important prerequisite for applications such as single-atom mass sensing [7,8,9] and fundamental studies of the quantum limit of mechanical motion [10]. Single-wall carbon nanotubes present a potentially defect-free nanomechanical system with extraordinary mechanical properties: in particular the high Young's modulus (E = 1.2 TPa) in combination with a very low mass density (ρ = 1350 kg/m3 ) [8,11,12,13]. While these favorable properties…”

Micromachined Resonant Frequency Tuning Unit for Torsional Resonator

“…The main advantage of the passive frequency methods is that they do not consume power to maintain the tuned state. On the other hand, the second approach does not rely on permanent structural modification, and therefore offers reversible and active tuning capabilities [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. Previous works for active frequency tuning utilized the electrostatic spring effect [ 14 , 15 ], the geometry of the capacitors [ 16 , 17 , 18 , 19 , 20 , 21 ], the thermal stressing effect [ 22 ], and thermal expansion [ 23 ].…”