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Carbon Nanotube Paddle Oscillators
Fabrication
The motivating vision of the field of nanoelectromechanical systems (NEMS) is the emergence of a host of high frequency, high sensitivity devices for use in telecommunication, optical switching and sensing technologies. These devices will also serve as nanolabs for fundamental investigations into physics of the mesoscale. The goal of high mechanical frequency along with high sensitivity (high Q) requires that actuators are very small (low mass), very stiff (high elastic modulus) and structurally defect free (low phonon scattering). Carbon nanotubes (CNTs) may provide several advantages over etched bulk semiconductors as flexural components. Their surfaces are atomically ordered, and they have low chemical reactivity, so they may not suffer from the surface-to-volume ratio issues that limit the quality factors of semiconductor- based devices. Here we report on successful fabrication and characterization of CNT oscillators including the first measurement of torsional compliance of a CNT.
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Suspended CNT
Paddle Structures:
The suspended torsional oscillators pictured on the left consist of a carbon nanotube torsional element and a metal test mass or “paddle”. They were fabricated using standard e-beam lithography then suspended through wet-etching followed by critical point drying. All scale bars are 1 micron in length. The metallic paddles consist of 10nm layer of Cr and a 80nm layer of Au. The multiwall carbon nanotubes are typically in the range of 15-40 nm in diameter.
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Distribution of Torsional Stress
In the figure on the left, a double paddle structure has been AFM manipulated such that the nearer paddle has been pressed to the underlying surface (where it remained adhered). The far paddle also shows a deflection indicating distribution of torsional strain along the length of the CNT.
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Characterization
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Torsional Compliance:
The torsional response of the fabricated paddles was characterized
using AFM force spectroscopy. Using our hybrid AFM/SEM systhttp://ced.ncsu.edu/nanoscale/em,
we placed the AFM tip at different points along the paddle and performed
force curves (see schematic left and SEM image below) deflecting the
paddles and measuring force simultaneously. |
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Figure on left shows a CNT paddle deflected by the AFM tip. The white line is included as a reference to emphasize the deflection.
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The plot on the left shows the raw force curve data. The three solid slopes show force curves taken at different points x along the paddle, while the dotted line shows the slope a force curve taken on the solid substrate. In the plot on the right, slope values are plotted as a function of position along the paddle. As expected the stiffness is low far from the pivot axis and increases as the pivot axis is approached. The solid line through the data is a theoretical fit (continuum mechanics) with the torsional spring constant k as a fitting parameter. Finding k, we can then back out a shear modulus of the CNT using standard continuum mechanics.
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The three curves in the right-hand plot are for the same paddle and indicate a that a stiffening is occurring as more deflections are performed (see discussion below). Once saturation of stiffness is achieved, shear modulus values for the CNT are calculated to be in the 1011 Pa range, which is consistent with theoretical values.
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Stiffening Behavior:
The plot on the left shows the increasing trend in the torsional stiffness as ~600 force curves are taken in succession. The break in the data indicates the point where the AFM tip had to be moved to a new position on the paddle (offset between raw data sets is most likely due to uncertainty in x position). Note that at ~400 force curves the stiffness appears to saturate. This behavior has been seen on every CNT-paddle oscillator tested. Its origin is still being investigated. One among several speculations is that the shells of the MWNT are becoming increasingly commensurate leading to larger effective torsional compliance.
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Next Steps: Resonance Frequency /Quality Factor Measurements
We are currently working on measurements of resonance frequency and Q using a variety of techniques. Our goal is to determine the limiting factors in Q, and to see how the stiffening behavior is correlated with resonance frequency. We will also continue tracking down the underlying mechanism of the stiffening behavior.
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