Introduction to Nanotechnology

82 PROPERTIES OF INDIVIDUAL NANOPARTICLES
CHANGE IN VALENCE ENERGY BAND LEVELS
WITH SIZE
BULK METAL LARGE METAL SMALL METAL
CLUSTER CLUSTER
(a) (b) (4
Figure 4.9. Illustration of how energy levels of a metal change when the number of atoms of the
material is reduced: (a) valence band of bulk metal; (b) large metal cluster of 100 atoms showing
opening of a band gap; (c) small metal cluster containing three atoms.
containing electrons, changes dramatically. The continuous density of states in the
band is replaced by a set of discrete energy levels, which may have energy level
spacings larger than the thermal energy ksT, and a gap opens up. The changes in the
electronic structure during the transition of a bulk metal to a large cluster, and then
down to a small cluster of less than 15 atoms, are illustrated in Fig. 4.9, The small
cluster is analogous to a molecule having discrete energy levels with bonding and
antibonding orbitals. Eventually a size is reached where the surfaces of the particles
are separated by distances which are in the order of the wavelengths of the electrons.
In this situation the energy levels can be modeled by the quantum-mechanical
treatment of a particle in a box. This is referred to as the quantum size effect.
The emergence of new electronic properties can be understood in terms of the
Heisenberg uncertainty principle, which states that the more an electron is spatially
confined the broader will be its range of momentum. The average energy will not be
determined so much by the chemical nature of the atoms, but mainly by the
dimension of the particle. It is interesting to note that the quantum size effect
occurs in semiconductors at larger sizes because of the longer wavelength of
conduction electrons and holes in semiconductors due the larger effective mass. In
a semiconductor the wavelength can approach one micrometer, whereas in a metal it
is in the order of 0.5nm.
The color of a material is determined by the wavelength of light that is absorbed
by it. The absorption occurs because electrons are induced by the photons of the
incident light to make transitions between the lower-lying occupied levels and higher
unoccupied energy levels of the materials. Clusters of different sizes will have
different electronic structures, and different energy-level separations. Figure 4.10
compares the calculated energy levels of some excited states of boron clusters Bg,
Bg, and BI2 showing the difference in the energy-level separations. Light-induced
transitions between these levels determines the color of the materials. This means
that clusters of different sizes can have different colors, and the size of the cluster can
be used to engineer the color of a material. We will come back to this when we
discuss semiconducting clusters.