3. The optical properties of these nanostructures are
determined by their electronic structure that
significantly differs for various morphologies since
electronic structure of the nanomaterials are very
much dependent on surface atoms.
Bulk materials energy levels are continuous, but in
the case of nanostructures, energy levels become
discrete; as mentioned before.
2. Electronic Structure and Optical Property
4. Bulk stable structure is constructed via the
formation of interatomic bonds from hybridization
between sp3 orbitals of neighboring atoms. After
hybridization, they give either bonding state or
antibonding state. The bonding states are fully
occupied whereas antibonding states are empty
and energy difference between them is defined as
band gap of the corresponding material.
5.
6. Energy of the bonding state is lower than that of
antibonding state. The formation of interatomic bonds
and splitting of sp3 orbitals occur everywhere within
the material.
However for an atom at the surface of the
nanoparticles, it has no neighbor at the vacuum side.
As a result, the unpaired bond of this surface atom
with intrinsic nature of sp3 hybridized state intrudes
toward the vacuum side and energy corresponding to
this lies between bonding and antibonding states.
7. These unpaired bonds are called dangling
bond.
These dangling bonds play a vital role in the
properties of the nanoparticles. These
unfavorable surface (since their energy is
greater than bonding state) states also act as
a driving force to determine the properties of
the nanoparticles.
8.
9. Experimentally, it is proved that band
gap of nanoparticles increases if its size is
reduced, i.e., absorption edge shifts
toward lower wavelength.
This shift is known as Blue shift.
10.
11. To understand these experimental results
theoretically, we consider electronic states near
valence band maxima and conduction band minima
which are mainly responsible for absorption and
emission process. Near edge states, electrons are
considered as free electrons, i.e., energy dispersive
relation for them is given by
12. The electronic state just below the valence band
maxima (Ek,VB) is given by:
The energy of the electronic state just above
conduction band minima (Ek,CB) is given by:
where EVBM and ECBM represents the energy associated
with valence band maxima and conduction minima.
13. The energy difference between them (Ek)
But, electrons are free and are spatially confined within a narrow
region space. So we may use “particle in box” model in three
dimensions for them.
