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Nanoelectromechanical Systems and Modeling
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INTRODUCTION
Nanoelectromechanical systems (NEMS) are made of electromechanical devices that have
critical dimensions from hundreds to a few nanometers. By exploring nanoscale effects,
NEMS present interesting and unique characteristics, which deviate greatly from their pre-
decessor microelectromechanical systems (MEMS). For instance, NEMS-based devices can
have fundamental frequencies in microwave range (∼100 GHz) [1]; mechanical quality fac-
tors in the tens of thousands, meaning low-energy dissipation; active mass in the femtogram
range; force sensitivity at the attonewton level; mass sensitivity up to attogram [2] and sub-
attogram [3] levels; heat capacities far below a “yoctocalorie” [4]; power consumption in
the order of 10 attowatts [5]; extreme high integration level, approaching 1012 elements per
square centimeter [1]. All these distinguished properties of NEMS devices pave the way
to applications such as force sensors, chemical sensors, biological sensors, and ultrahigh-
frequency resonators.
NANOELECTROMECHANICAL SYSTEMS
Carbon Nanotubes
Carbon nanotubes exist as a macromolecule of carbon, analogous to a sheet of graphite
rolled into a cylinder. They were discovered by Sumio Iijima in 1991 and are a subset of the
family of fullerene structures [13]. The properties of the nanotubes depend on the atomic
arrangement (how sheets of graphite are rolled to form a cylinder), their diameter, and their
length. They are light, stiff, flexible, thermally stable, and chemically inert. They have the
ability to be either metallic or semiconducting depending on the “twist” of the tube, which
is called “chirality” or “helicity.” Nanotubes may exist as either single-walled or multiwalled
structures. Multiwalled carbon nanotubes (MWNTs) (Fig. 2(B)) are simply composed of
multiple concentric single-walled carbon nanotubes (SWNTs) (Fig. 2(A)) [14]. The spacing
between the neighboring graphite layers in MWNTs is ∼0.34 nm. These layers interact with
each other via van der Waals forces.
Fabrication Methods
The fabrication processes of NEMS devices can be categorized according to two approaches.
Top-down approaches, that evolved from manufacturing of MEMS structures, use submicron
lithographic techniques, such as electron-beam lithography, to fabricate structures from bulk
materials, either thin films or bulk substrates. Bottom-up approaches fabricate the nanoscale
devices by sequentially assembling of atoms and molecules as building blocks. Top-down
fabrication is size limited by facts such as the resolution of the electron-beam lithography,
etching-induced roughness, and synthesis constraints in epitaxially grown substrates. Sig-
nificant interest has been shown in the integration of nanoscale materials such as carbon
nanotubes and nanowires, fabricated by bottom-up approaches, to build nanodevices. Most
of the nanodevices reported so far in the literature are obtained by “hybrid” approaches, that
is, combination of bottom-up (self assembly) and top-down (lithographic) approaches [24].
One of the key and most challenging issues of building carbon nanotubes–based or
nanowires-based NEMS is the positioning of nanotubes or nanowires at the desired locations
with high accuracy and high throughput. Reported methods of manipulation and positioning
of nanotubes are briefly summarized in the following section.
Random Dispersion Followed by E-Beam Lithography
After purification, a small aliquot of a nanotube suspension is deposited onto a substrate.
The result is nanotubes randomly dispersed on the substrate. Nanotubes on the substrate
are imaged inside a scanning electron microscope (SEM) and then this image is digitized
and imported to a mask-drawing software, where the mask for the subsequent electron-
beam lithography is designed. In the mask layout, pads are designed to superimpose over
the carbon nanotubes. Wet etching is employed to remove the material under the carbon
nanotubes to form freestanding nanotube structures. This process requires an alignment
capability in the lithographic step with an accuracy of 0.1 m or better. This method was
firstly employed to make nanotube structures for mechanical testing [25, 26]. The reported
NEMS devices based on this method include nanotube–based rotational actuators [9] and
nanowire-based resonators [24].
Detecting Motion
The most straightforward method is by direct observation of the motion under electron
microscopes [7, 8, 56, 57]. This visualization method, typically with resolution in the nano-
meter scale, projects the motion in the direction to be perpendicular to the electron beam.
Limitations in depth of focus requires that the nano-object motion be primarily in a plane,
which normally is coaxial with the electron beam. Electron tunneling is a very sensitive
method that can detect subnanometer motion by the exponential dependence of the electron
tunneling current on the separation between tunneling electrodes. Therefore, this technique
is widely used in NEMS motion detection [5, 12]. Magnetomotive detection is a method
based on the presence of an electrostatic field, either uniform or spatially inhomogeneous,
through which a conductor is moved. The time-varying flux generates an induced electromo-
tive force in the loop, which is proportional to the motion [24, 52, 58–60]. The displacement
detection sensitivity of this technique is less than 1 Å [61]. It is known that carbon nanotubes
can act as transistors; as such they can be used to sense their own motion [12, 62]. Capac-
itance sensors have been widely used in MEMS. They can also be used in NEMS motion
sensing with a resolution of a few nanometers [54], and the resolution can be potentially
increased to Angstrom range provided that the capacitance measurement can be improved
by one order of magnitude.
MODELING OF NANOELECTROMECHANICAL
SYSTEMS DEVICES
The design of NEMS depends on a thorough understanding of the mechanics of the devices
themselves and the interactions between the devices and the external forces/fields. With the
critical dimension shrinking from micron to nanometer scale, new physics emerges so that the
theory typically applied to MEMS does not immediately translated to NEMS. For example,
van der Waals forces from atomic interactions play an important role in NEMS, while they
can be generally neglected in MEMS. The behavior of materials at nanometer scale begins
to be atomistic rather than continuous, giving rise to anomalous and often nonlinear effects,
for example,