Nanotechnology-Enabled Sensors

146 Chapter 4: Nano Fabrication and Patterning Techniques
where Edes is the desorption energy of the desorbing species and v is the
vibrational frequency of the adsorbed species on the surface. Ds is described
by:
( − E / kT )
a0v
exp s
Ds
= , (4.3)
2
where a0 is the growth species’ largest dimension, and Es is surface diffusion
activation energy. Consequently, the mean diffusion distance, X, is
defined as:
X = 2D
τ . (4.4)
X plays an important role in the formation of nanostructures as it is used
for the calculation of accommodation coefficient, α (see Eq. (4.)).
As we learned earlier, kinks, steps and other types of anomalies on a surface
tend to reduce the surface energy and thus making them energetically
favorable for the adsorption of the growth species. If X is longer than the
distance between the anomalies, the growth species has a chance to adsorb
on the surface of the substrate. However, if the distance between anomalies
is shorter then the growth species, it can escape the surface and materials
growth will not occur. In the formation of one-dimensional structures, either
anomalies with the right separations from each other or crystals with
different surface facets are needed. After the formation of a seed nucleus
on the surface, the growth will continue on the facet (or facets) with the
lower energy.
Several theories have been proposed for describing the formation of onedimensional
structures in the evaporation-condensation process such as:
axial screw dislocation, formation of micro-twins, stacking faults etc.
However, most of them fail to present a general idea which can predict the
growth in different situations. 30
Interestingly, the growth rate of nanowires exceeds the theoretical condensation
rate as calculated using Eq. (4.) with the accommodation coefficient
of one. This translates into the fact that the growth of such nanowires
is the fastest type of growth which can occur on a surface. A dislocationdiffusion
theory as proposed by Dittmar et al has been proposed to describe
such a phenomenon. 31
It is believed that one of the first reports on the evaporationcondensation
growth of mercury nanowires was presented by Sears in
1955. 32 He developed mercury nanowires with the cross sectional diameters
of 200 nm and the length of several mm using a condensation temperature
of -50°C. The growth rate was 1.5 μm/sec for a supersaturation, α,
value of 100.
s
s