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Bending-mode vibrations of carbon nanotube resonators were mechanically detected in air at atmospheric pressure by means of a novel scanning force microscopy method. The fundamental and higher order bending eigenmodes were imaged at up to 3.1 GHz with subnanometer resolution in vibration amplitude. The resonance frequency and the eigenmode shape of multiwall nanotubes are consistent with the elastic beam theory for a doubly clamped beam. For single-wall nanotubes, however, resonance frequencies are significantly shifted, which is attributed to fabrication generating, for example, slack. The effect of slack is studied by pulling down the tube with the tip, which drastically reduces the resonance frequency. DOI: 10.1103/PhysRevLett.99.085501 PACS numbers: 85.85.+j, 73.63.Fg, 81.16.Rf, 85.35.Kt Carbon nanotubes offer unique opportunities as highfrequency mechanical resonators for a number of applications. Nanotubes are ultralight, which is ideal for ultralow mass detection and ultrasensitive force detection [1,2]. Nanotubes are also exceptionally stiff, making the resonance frequency very high. This is interesting for experiments that manipulate and entangle mechanical quantum states [3][4][5]. However, mechanical vibrations of nanotubes remain very difficult to detect. Detection has been achieved with transmission or scanning electron microscopy [1,6 -8] and field emission [9]. More recently, a capacitative technique has been reported [10 -12] that allows detection for nanotubes integrated in a device, and is particularly promising for sensing and quantum electromechanical experiments. A limitation of this capacitive technique is that the measured resonance peaks often cannot be assigned to their eigenmodes. In addition, it is often difficult to discern resonance peaks from artefacts of the electrical circuit. It is thus desirable to develop a method that allows the characterization of these resonances.In this Letter, we demonstrate a novel characterization method of nanotube resonator devices, based on mechanical detection by scanning force microscopy (SFM). This method enables the detection of the resonance frequency (f res ) in air at atmospheric pressure and the imaging of the mode shape for the first bending eigenmodes. Measurements on single-wall nanotubes (SWNT) show that the resonance frequency is very device dependent, and that f res dramatically decreases as slack is introduced. We show that multiwall nanotube (MWNT) resonators behave differently from SWNT resonators. The resonance properties of MWNTs are much more reproducible, and are consistent with the elastic beam theory for a doubly clamped beam without any internal tension.An image of one nanotube resonator used in these experiments is shown in Fig. 1(a). The resonator consists of a SWNT grown by chemical-vapor deposition [13] or a MWNT synthesized by arc-discharge evaporation [14]. The nanotube is connected to two Cr=Au electrodes patterned by electron-beam lithography on a high-resistivity Si substrate (10 k cm) with a 1 m thermal silicon...

Local oxidation of silicon surfaces by atomic force microscopy is a very promising lithographic approach at nanometer scale. Here, we study the reproducibility, voltage dependence, and kinetics when the oxidation is performed by dynamic force microscopy modes. It is demonstrated that during the oxidation, tip and sample are separated by a gap of a few nanometers. The existence of a gap increases considerably the effective tip lifetime for performing lithography. A threshold voltage between the tip and the sample must be applied in order to begin the oxidation. The existence of a threshold voltage is attributed to the formation of a water bridge between tip and sample. It is also found that the oxidation kinetics is independent of the force microscopy mode used (contact or noncontact).

This paper describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation that remains valid up to large displacements in the case of electrostatically actuated nanocantilevers. This purely analytical model takes into account the fringing field effects which are significant for thin resonators. Analytical simulations show very good agreement with experimental electrical measurements of silicon nanodevices using wafer-scale nanostencil lithography (nSL), monolithically integrated with CMOS circuits. Close-form expressions of the critical amplitude are provided in order to compare the dynamic ranges of NEMS cantilevers and doubly clamped beams. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility of driving the cantilever beyond its critical amplitude. Consequently, the sensor performance can be enhanced by being optimally driven at very large amplitude, while maintaining linear behavior.

We report STM-induced desorption of H from Si(100)-H(2×1) at negative sample bias. The desorption rate exhibits a power-law dependence on current and a maximum desorption rate at −7 V. The desorption is explained by vibrational heating of H due to inelastic scattering of tunneling holes with the Si-H 5σ hole resonance. The dependence of desorption rate on current and bias is analyzed using a novel approach for calculating inelastic scattering, which includes the effect of the electric field between tip and sample. We show that the maximum desorption rate at −7 V is due to a maximum fraction of inelastically scattered electrons at the onset of the field emission regime.