Nanotechnology-Enabled Sensors

144 Chapter 4: Nano Fabrication and Patterning Techniques
It is possible to change the Gibbs free energy locally through the introduction
of surface anomalies such as impurities, kinks and ledges. In such
cases, the anomalies will play an important role as the nucleation sites
where the growth species are initially adsorbed. Different facet of the substrate
crystal, addition of a catalyst on the surface and changing the local
pressure can also alter the Gibbs free energy of the deposition sites.
The existence of different faces on a surface substrate produces different
atomic densities and ‘loose’ or ‘unsatisfied’ bonds. This results in isolated
surface energies, which in turn determines the growth rate and growth
mechanism of the thin film at the facet site.
Hartman and Perdok 29 developed periodic bond chain (PBC) theory to
categorize surfaces into one of three types: flat, stepped, and kinked.
Even a flat surface on the atomic scale is not truly flat, due to interatomic
effects and localization. Such discontinuities change the Gibbs free
energy of the deposition site. Sites of low energy are favourable for interaction
with the growth species and are responsible for growth on a flat surface.
According to PBC theory adsorbed atoms (or adatoms) of a growth
species form a single chemical bond with flat surfaces, while stepped and
kinked surfaces may form three and four chemical bonds, respectively. 29
Evaporation-condensation growth
This method (also referred to Vapor-Solid, VP) is based on the decrease of
Gibbs free energy produced by surface clusters forming or the decrease in
supersaturation (change of pressure on the surface). The condensation on
the surface can be purely physical; however, chemical reactions can also
participate in the process. Generally nanostructures which are grown using
this process, are fairly single crystalline. However, condensation on
substrates of similar materials with different faces can also result in nanostructures
with varied dimensions and crystals structures. Impurities and
imperfections on the substrate may also produce special growth directions
for the nanostructures.
The growth rate is defined with the condensation rate, J. This rate depends
on the vapour pressure P, the accommodation coefficient α, the
supersaturation of growth species in vapour σ = (P-P0)/P0 (with P0 the
equilibrium vapour pressure), the substrate temperature T in Kelvin,
the atomic mass of the growth species m, and Boltzmann’s constant k and
is defined as: 28
ασP0
J = . (4.1)
2πmkT