No Voltage

POSmVE VOLTAGE

Figure 13.6. Illustration of an actuator consisting of two sheets of single-walled nanopaper held together by insulating double-stick Scotch tape. The figure shows the positive-voltage state (right), the resting state (center), and the negative-voltage state (left). [Adapted from R. H. Baughman et al., Science 284, 340 (1999).]

consist of three fibers aligned with their axes parallel and in contact. The outer two tubes would be metallic and the inner tube insulating.

Although electron-beam lithography can be used to fabricate silicon structures less than 10 nm in size, nanomachines have not been produced to any large extent A number of difficulties must be overcome before significant progress can be made. The first is the problem of communicating with and sensing the motion of the nanoscale devices. The second obstacle is that littie is known or understood about the mechanical behavior of objects, which have up to 10% of their atoms on or near the surface.

The resonant frequency f0 of a clamped beam is given by where £ is the elastic modulus, p is the density, b is the thickness of the beam, and L is the beam length. Experimental verification of the scaling of the frequency with l/L2 is shown in Fig. 13.2 for poly silicon beams of micrometer dimension. Notice that in the micrometer range the frequencies are in the hundreds of kilohertz (> 105 cycles per second). Now a beam having a length of 10 nm and thickness of 1 nm will

have a resonant frequency 105 times greater, of the order of 20-30 GHz (2-3 x 1010 cycles per second). As the frequency increases, the amplitude of vibratM* decreases, and in this range of frequencies the displacements of die beam can range from a picometer (10_12m) to a femtometer (10-15m).

These high frequencies and small displacements are very difficult, if not impossible, to detect. Optical reflection methods such as those used in the micrometer range on the cantilever tips of scanning tunneling microscopes are not applicable because of the diffraction limit. This occurs when the size of the object from which light is reflected becomes smaller than the wavelength of the light. Transducers are generally used in MEMS devices to detect motion. The MEMs accelerometer shown in Fig. 13.1 is an example of the detection of motion using a transducer. In the accelerometer mechanical motion is detected by a change in capacitance, which can be measured by an electrical circuit. It is not clear that such a transducer sensor can be built that can detect displacements as small as 10-15 to 10-l2m, and do so at frequencies up to 30GHz. These issues present significant obstacles to the development of NEMS devices.

There are, however, some noteworthy advantages of NEMS devices that make it worthwhile to pursue their development. The small effective mass of a nanometer-sized beam renders its resonant frequency extremely sensitive to slight changes in its mass. It has been shown, for example, that die frequency can be affected by adsorption of a small number of atoms on die surface, which could be the basis for a variety of vety high-sensitivity sensors.

A weight on a spring would oscillate indefinitely with the same amplitude if there were no friction. However, because of air resistance, and the internal spring friction, this does not happen. Generally the fiictional or damping force is proportional to the velocity dx/dt of the oscillating mass M. The equation of motion of the spring is

where K is the spring of constant.

The solution X(m) to this equation for a small damping factor b is

with the frequency w given by

Equation (13.3) describes a system oscillating at a fixed frequency a> with an amplitude exponentially decreasing in time. The displacement as a function of time is plotted in Fig. 13.7a. For a clamped vibrating millimeter-sized beam, a major ne cos lot (8 = 0)

0 0

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