Guozhong Cao. Nanostructures & Nanomaterials: Synthesis, Properties & Applications
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106
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Chapter
4
One-Dimensional
Nanost ructu res: Nanowi res
and Nanorods
4.1.
Introduction
One-dimensional nanostructures have been called by a variety of names
including: whiskers, fibers or fibrils, nanowires and nanorods. In many
cases, nanotubules and nanocables are also considered one-dimensional
structures. Although whiskers and nanorods are in general considered
to be shorter than fibers and nanowires, the definition is oAen a little
arbitrary. In addition, one-dimensional structures with diameters ranging
from several nanometers to several hundred microns were referred to
as whiskers and fibers in the early literature, whereas nanowires and
nanorods with diameters not exceeding a few hundred nanometers are
used predominantly in the recent literature. One will find, from reading
this chapter, the fact that many fundamental understandings and tech-
niques of growth of one-dimensional nanostructures are based on the early
work on the growth of whiskers and fibers,
albeit
with less emphasis
on nanometer scale. In this chapter, various terms of one-dimensional
structures will be used interchangeably, though nanowires in general have
a high aspect ratio than that of nanorods.
Many techniques have been developed in the synthesis and formation of
one-dimensional nanostructured materials, though some techniques have
been explored extensively, while others have attracted far less attention.
110
One-Dimensional Nanostructures: Nanowires and Nanorods
111
These techniques can
be
generally grouped into four categories:
(1)
Spontaneous growth:
(a) Evaporation (or dissolution)-condensation
(b) Vapor (or solution)-liquid-solid (VLS or SLS) growth
(c) Stress-induced recrystallization
(a) Electroplating and electrophoretic deposition
(b) Colloid dispersion, melt, or solution filling
(c) Conversion with chemical reaction
(2)
Template-based synthesis:
(3)
Electrospinning
(4)
Lithography
Spontaneous growth, template-based synthesis and electrospinning are
considered as a bottom-up approach, whereas lithography is a top-down
technique. Spontaneous growth commonly results in the formation of
single crystal nanowires or nanorods along a preferential crystal growth
direction depending on the crystal structures and surface properties of the
nanowire materials. Template-based synthesis mostly produces polycrys-
talline or even amorphous products. All the above techniques for the prepa-
ration of one-dimensional nanostructured materials will be discussed in
this chapter, following the above order just for the sake of clarity. Litho-
graphy will be discussed briefly only; more detail and general discussion
on lithography will be presented in Chapter
7.
Similar to the previous chap-
ter, this chapter will cover all the nanowires, nanorods and nanotubules
of
various materials including metals, semiconductors, polymers and insulat-
ing oxides. This chapter focuses on the fundamentals and principles
of
the
major synthesis methods. For detailed information on specific materials,
the readers are referred to a comprehensive review on the synthesis, char-
acterization and applications of one-dimensional nanostructures. Carbon
nanotubes, as a special family of nanomaterials, deserve special attention
and, therefore, will be discussed separately later on in Chapter
6.
4.2.
Spontaneous
Growth
Spontaneous growth is a process driven by the reduction of Gibbs free
energy or chemical potential. The reduction
of
Gibbs free energy is com-
monly realized by phase transformation or chemical reaction or the
release
of
stress. For the formation of nanowires or nanorods, anisotropic
growth is required, i.e. the crystal grows along a certain orientation faster
than other directions. Uniformly sized nanowires, i.e. the same diameter
112
Nanostructures and Nanomaterials
along the longitudinal direction of a given nanowire, can be obtained
when crystal growth proceeds along one direction, whereas no growth
along other directions. In spontaneous growth, for given material and
growth conditions, defects and impurities on the growth surfaces can play
a significant role in determining the morphology of the final products.
4.2.1.
Evaporation
(dissolution)-condensation
growth
4.2.1
.l
.
Fundamentals
of
evaporation (dissolution)-
condensation
growth
Evaporation-condensation process is also referred to as a vapor-solid
(VS)
process; however, the discussion in this section will not only be lim-
ited to simple
evaporation-condensation
process. Chemical reactions
among various precursors may be involved to produce desired materials.
Of course, the growth of nanorods from solution is also included. The
driving force for the synthesis of nanorods and nanowires by spontaneous
growth is a decrease in Gibbs free energy, which arises from either recrys-
tallization or a decrease in supersaturation. Nanowires and nanorods
grown by
evaporation-condensation
methods are commonly single crys-
tals with fewer imperfections. The formation of nanowires, nanorods
or nanotubules through evaporation (or
dissolutiontcondensation
is due
to the anisotropic growth. Several mechanisms are known to result in
anisotropic growth, for example:
(1)
Different facets in a crystal have different growth rate. For example,
in silicon with a diamond structure, the growth rate of
{ 11
1
facets is
smaller than that of
{
1
lo}.
(2)
Presence of imperfections in specific crystal directions such as screw
dislocation.
(3)
Preferential accumulation of or poisoning by impurities on specific
facets.
Before discussing the growth
of
various nanowires by evaporation-
condensation method in detail, let us first review the fundamentals of
crystal growth. Crystal growth can be generally considered as a heteroge-
neous reaction, and a typical crystal growth proceeds following the
sequences, as sketched in Fig.
4.1
:
(1)
Diffusion of growth species from the bulk (such
as
vapor or liquid
phase) to the growing surface, which, in general, is considered to
proceed rapid enough and, thus, not at a rate limiting process.
One-Dimensional Nanostructures: Nanowires and Nanorods
113
(2)
Adsorption and desorption of growth species onto and from the grow-
ing surface. This process can be rate limiting, if the supersaturation or
concentration of growth species is low.
(3)
Surface diffusion of adsorbed growth species. During surface diffu-
sion, an adsorbed species may either be incorporated into a growth
site, which contributes to crystal growth, or escape from the surface.
(4)
Surface growth by irreversibly incorporating the adsorbed growth
species into the crystal structure. When a sufficient supersaturation or
a high concentration
of
growth species is present, this step will be the
rate-limiting process and determines the growth rate.
(5)
If
by-product chemicals were generated on the surface during
the growth, by-products would desorb from the growth surface,
so
that growth species can adsorb onto the surface and the process
can continue.
(6)
By-product chemicals diffuse away from the surface
so
as to vacate
the growth sites for continuing growth.
For most crystal growth, rate-limiting step
is
either adsorption-desorption
of growth species on the growth surface (step
2)
or surface growth (step
4).
When step
2
is rate limiting, the growth rate is determined by condensation
rate,
J
(atoms/cm*sec), which is dependent on the number
of
growth
species adsorbed onto the growth surface, which is directly proportional to
the vapor pressure or concentration,
P,
of the growth species in the vapor
as given by:
(6)
Diffusion
of
by-products
Growth
species
in the bulk
0
I
I
I
Solid
Surface
I
Fig.
4.1.
Schematic illustrating six steps in crystal growth, which can be generally considered
as a heterogeneous reaction, and a typical crystal growth proceeds following the sequences.
114
Nunostructures
and
Nanomateriuls
where
01
is the accommodation coefficient,
u
=
(P-Po)/Po
is the supersat-
uration of the growth species in the vapor in which
Po
is the equilibrium
vapor pressure of the crystal at temperature
T,
rn
is
the atomic weight of
the growth species and
k
is Boltzmann constant.
(Y
is the fraction of
impinging growth species that becomes accommodated on the growing
surface, and is a surface specific property.
A
surface with a high accom-
modation coefficient will have a high growth rate as compared with low
(Y
surfaces. A significant difference in accommodation coefficients in dif-
ferent facets would result in anisotropic growth. When the concentration
of
the growth species is very low, the adsorption is more likely
a
rate-
limiting step. For a given system, the growth rate increases linearly with
the increase in the concentration of growth species. Further increase in the
concentration of growth species would result in a change from an adsorp-
tion limited to surface growth limited process. When the surface growth
becomes a limiting step, the growth rate becomes independent of the con-
centration of growth species as schematically shown in Fig.
4.2.
A high
concentration or vapor pressure of growth species in the vapor phase
would increase the probability of defect formation, such as impurity inclu-
sion and stack faults. Further, a high concentration may result in a sec-
ondary nucleation on the growth surface or even homogeneous nucleation,
which would effectively terminate the epitaxial or single crystal growth.
An impinging growth species onto the growth surface can be described
in terms of the residence time and/or difhsion distance before escaping
Adsorption
limited
process
t
rface
growth
limited process
b
Concentration
of
growth
species
Fig.
4.2.
Relation between growth rate and reactant concentration. At low concentration,
growth is diffusion limited and thus increases linearly with increasing reactant concentra-
tion. At high concentration, surface reaction is the limit step and thus the growth rate
becomes independent
of
reactant concentration.
One-Dimensional Nanostructures: Nanowires and Nanorods
115
back to the vapor phase. The residence time,
T,,
for a growth species on
the surface is described by:
7,
=
-
1
expk)
v
(4.2)
where
v
is the vibrational frequency of the adatom,
i.e.
adsorbed growth
species, on the surface (typically 1012sec-'), and
Edes
is the desorption
energy required for the growth species escaping back to the vapor. While
residing on the growth surface, a growth species will diffuse along the sur-
face with the surface diffusion coefficient,
D,,
given by:
0,
=
-
1
aov
exp(
$)
2
(4.3)
where
E,
is the activation energy for surface diffusion and
a.
is the size of
the growth species.
So
the mean diffusion distance,
X,
for a growth species
from the site of incidence:
X
=
fiDS7,
=
a.
exp(
Edes
kT
-
E,
)
(4.4)
It is clear that in a crystal surface, if the mean diffusion distance is far
longer than the distance between two growth sites such as kinks or ledges,
all adsorbed growth species will be incorporated into the crystal structure
and the accommodation coefficient would be unity. If the mean diffusion
distance is far shorter than the distance between growth sites, all adatoms
will escape back to the vapor and the accommodation coefficient will be
zero. The accommodation coefficient is dependent on desorption energy,
activation energy
of
surface diffusion and the density of growth sites.
When step
2
proceeds sufficiently rapid, surface growth, i.e. step
4,
becomes
a
rate-limiting process. In Chapter
2,
we have discussed the fact
that in a crystal, different facets have different surface energy. Different
facets in a given crystal have different atomic density and atoms on differ-
ent facets have
a
different number of unsatisfied bonds (also referred to
as
broken or dangling bonds), leading to different surface energy. Such a dif-
ference in surface energy or the number of broken chemical bonds leads to
different growth mechanisms and varied growth rates. According to Periodic
Bond Chain
(PBC)
theory developed by Hartman and Perdok,* all crystal
facets can be categorized into three groups based on the number of broken
periodic bond chains on
a
given facet: flat surface, stepped surface and
kinked surface. The number of broken periodic bond chains can be under-
stood as the number of broken bonds per atom on a given facet in a simpli-
fied manner. Let us first review the growth mechanisms on a flat surface.