High Q resonators are a critical component of stable, low-noise communication systems, radar, and precise timing applications such as atomic clocks. In electronic resonators based on Si integrated circuits, resistive losses increase as a result of the continued reduction in device dimensions, which decreases their Q values. On the other hand, due to the mechanical construct of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators, such loss mechanisms are absent, enabling higher Q-values for both BAW and SAW resonators compared to their electronic counterparts. The other advantages of mechanical resonators are their inherently higher radiation tolerance, a factor that makes them attractive for NASA’s extreme environment planetary missions, for example to the Jovian environments where the radiation doses are at hostile levels. Despite these advantages, both BAW and SAW resonators suffer from low resonant frequencies and they are also physically large, which precludes their integration into miniaturized electronic systems.

Because there is a need to move the resonant frequency of oscillators to the order of gigahertz, new technologies and materials are being investigated that will make performance at those frequencies attainable. By moving to nanoscale structures, in this case vertically oriented, cantilevered carbon nanotubes (CNTs), that have larger aspect ratios (length/thickness) and extremely high elastic moduli, it is possible to overcome the two disadvantages of both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators.

Nano-electro-mechanical systems (NEMS) that utilize high aspect ratio nanomaterials exhibiting high elastic moduli (e.g., carbon-based nanomaterials) benefit from high Qs, operate at high frequency, and have small force constants that translate to high responsivity that results in improved sensitivity, lower power consumption, and improved tunablity. NEMS resonators have recently been demonstrated using top-down, lithographically fabricated approaches to form cantilever or bridge-type structures. Top-down approaches, however, rely on complicated and expensive e-beam lithography, and often require a release mechanism. Resonance effects in structures synthesized using bottom-up approaches have also recently been reported based on carbon nanotubes, but such approaches have relied on a planar two-dimensional (2D) geometry. In this innovation, vertically aligned tubes synthesized using a bottom-up approach have been considered, where the vertical orientation of the tubes has the potential to increase integration density even further.

The simulation of a vertically oriented, cantilevered carbon nanotube was performed using COMSOL Multi-physics, a finite element simulation package. All simulations were performed in a 2D geometry that provided consistent results and minimized computational complexity. The simulations assumed a vertically oriented, cantilevered nanotube of uniform density (1.5 g/cm3). An elastic modulus was assumed to be 600 GPa, relative permittivity of the nanotube was assumed to be 5.0, and Poisson’s ratio was assumed to be 0.2. It should be noted that the relative permittivity and Poisson’s ratio for the nanotubes of interest are not known accurately. However, as in previous simulations, the relative permittivity and Poisson’s ratios were treated as weak variables in the simulation, and no significant changes were recognized when these variables were varied.

Of interest in the simulations of a CNT resonator were the structural strain and deflection of the nanotube, and the electrostatic interactions between the nanotube and nanomanipulator probe. Structural boundary conditions were arranged such that the exposed lengths and tip of the nanotube were allowed to move freely while all other surfaces were held fixed (including the nanotube base). These conditions simulated a fixed, cantilevered beam in a domain adjacent to a nanomanipulator probe of infinite elastic modulus. Electrostatic boundary conditions were chosen such that the nanotube was grounded, an AC voltage with DC bias was applied to the surface of the nanoprobe adjacent to the nanotube, and all other boundaries in the system were selected such that no electrical charge exists on, or outside of, those surfaces. The solution domain was simulated as a vacuum. Preliminary experiments have suggested that electromechanical coupling can occur between a scanning electron microscope (SEM) beam and a vertically oriented, cantilever carbon nanofiber (CNF) causing the CNF to mechanically resonate with displacements two or three times larger than the tube diameters.

This work was done by Anupama B. Kaul and Larry W. Epp of Caltech and Leif Bagge of the University of Texas for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it..

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:

Innovative Technology Assets Management JPL Mail Stop 202-233 4800 Oak Grove Drive

Pasadena, CA 91109-8099 E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Refer to NPO-47238, volume and number of this NASA Tech Briefs issue, and the page number.


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This article first appeared in the June, 2011 issue of NASA Tech Briefs Magazine.

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