Hierarchical Field Emission Devices - Hierarchical Nanostructures for Energy Devices - page 233

of materials and geometries. In the simplest model, for emitters of height
h with a tip of radius of curvature r, it can be expressed as b ¼ h/r,
which is often called 'aspect ratio' (AR). Alternatively, the value of b can be
determined from the current-voltage measurements, via calculation of the
slope of the ln(J/E 2 ) vs (1/E) plot (known as FN plot) in eqn (10.4). However, in
most cases, the value obtained may be physically unrealistic in the sense that
it is orders of magnitude higher than the emitter AR. As can be seen from
eqn (10.3), the emission performance of an emitter can be enhanced by
increasing the AR and in series the enhancement factor b.
The highest current density attainable, lower turn-on voltage (defined as
the applied bias needed to obtain measurable current), increased b, stability
of the FE current and lifetime are the figures of merit for FE cathodes.
Among the important parameters affecting the current stability are the
residual gas pressure and atom adsorption and/or desorption causing local
work function variations. Ease of fabrication, high charge carrier mobility
and electrical conductivity are also important for the applicability of FE
sources in electronic devices.

d n 3 r 4 n g | 0

10.2 Hierarchical Field Emission Cathodes
A critical parameter for a FE cathode performance is the field enhancement
factor b which can be enhanced by increasing the 'AR', h/r of the
emitters. Owing to their unique geometries of small curvature radius, one-
dimensional (1D) nanostructures including carbon nanotubes (CNTs)
nanowires and nanofibers have attracted significant interest for their
potential field emission (FE) applications. Besides this, two-dimensional
(2D) nanostructures such as carbon nanowalls, graphene and other 2D
nanosheets should also give rise to high geometric field enhancement. To
further increase b thus enhance the FE capability of various 1D or 2D
nanostructures, different approaches have been proposed. Among the most
promising, one that has been frequently employed recently is based on
hierarchical development of the emitting material, for example via using a
micron-sized structured substrate and subsequently growing nanostructures
onto it (Figure 10.1b). This approach offers the advantages of not only
further increasing the enhancement factor b of the emitters, but also
significantly increasing the effective electron emitting area and therefore the
density of the emitting sites.
The effect of regular and random variations in emitter morphology was
first addressed by Atlan et al. 5 According to this work, the geometric
mismatch among the protruding structures and thus the fractal dimension
of the emitting surface determine the degree of field enhancement while the
total emission current is determined by the geometry of protrusions. Zhirnov
et al. considered an analytical model to address emission from small
protrusions on the surface. 6 According to this model, the emitting surface
may be thought of as a number of primary structures with a height of h 1 and
sharpness of r 1 , decorated by tiny emitters with a height of h 2 and sharpness

.