They potential energy. Paramagnetic QDs: certain materials are

They are called dots because they are tiny, so small that it is
effectively concentrated into itself/a single point. They are 0D
semiconductors, and have been referred to as ‘artificial atoms’.

Drummen, G., 2010: the term ‘quantum dots’ denotes nanocrystalline
semiconducting fluorophores, whose excitons are confined in all three spatial
dimensions – quantum confinement: strict confinement of electrons and holes
when the nanoparticle radius is below the exciton Bohr radius – and have
typical diameters of 2-20nm.

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Tytus, et al. 2008:
Self-assembled QDs are formed as a result of strain between two lattices with
significantly mismatched lattice constants (Stransly-Krastanow
method).

 

In quantum dots, the core determines
their optical properties, and the properties of the shell strengthens their
photostability.

 

The structural properties of QDs:

Semi-conducting
crystallites, with dimensions smaller than the exciton Bohr radius
Crystal-like
self-assembly into ordered superlattices

 

The physical (physics) properties of QDs:

Physical
properties: fluorescent properties, such as high quantum yield,
photostability, broad absorption spectra, and size-dependent
emission-tunability
Light-harvesting
applications (e.g. photodetectors or solar cells)

Three
limiting charge carrier localization regimes in core/shell semiconductors.
The energy of the bulk conduction and valence band gaps sets the potential
energy of the charge carriers, while the effective mass from the bulk band
structure determines the kinetic energy. The wave functions of the
lowest-energy electron and hole states can be seen.

The
band edges are the limits of the core and shell.

The charger carriers tend to localize
in the part of the hetero-NC with the lowest potential energy.

Paramagnetic
QDs: certain materials are weakly attracted by an externally applied
magnetic field, and form internal, induced magnetic fields in the
direction of the applied magnetic field. They have relative magnetic
permeability slightly bigger than 1 (i.e. small positive magnetic
susceptibility) and hence attracted to magnetic fields.
Diamagnetic
materials are repelled by magnetic fields, and form induced magnetic
fields in the direction opposite to that of the applied magnetic field.

 

As
the excitation photon energy increases (and wavelength decreases) the QD
absorption likewise increases suggesting that extremely large effective Stoke’s
shift (spectral intervals between excitations and emission maxima) are
possible. Large molar absorption cross-sections = effective brightness per
probe particle is superior

 

The chemical properties of QDs:

Inorganic
crystallites and organic surfactants
Core-shell
structures; core material coated with shell material
Surface
functionalization and development of flexible bioconjugation techniques.

Chemical adaptation of the surface not
only renders it water-soluble, but allows biocompatilization and
functionalization, but also eliminates photobleaching by physically excluding
interaction of the excited state particle with molecular oxygen and thus
prevents formation of ROS, such as singlet oxygen.

 

The optical properties of QDs:

Strong
light absorbance
Size-tunable
emission
Bright
fluorescence/high quantum yield
Narrow
symmetric emission bands
High
photostability
Low
photobleaching rates

And broad absorption spectrum allows
the simultaneous excitation of QDs of all sizes by a single excitation light
source in the UV to violet part of the spectrum. Drummen, G., 2010

 

Different types of QDs:

Type
I hetero-NC (e.g. CdSe/ZnS), both charge carriers co-localize in one part.

These trap electrons and holes
simultaneously. They have contravariant band layout.

Type
I 1/2 (e.g. CdSe/CdS), one charge carrier delocalizes over the entire NC
while the other one is localized in one part.
Type
II (e.g. CdSe/ZnTe), two charge carriers are spatially separated, each in
a different part, forming a spatially indirect exciton.

These empty dots attract only type of
charged carrier and repel the other. They have covariant band layout.

 

 
Conduction bands

Native ligands have been exchanged with small organic or inorganic
linkers. The native ones had wide gaps between their highest occupied and
lowest unoccupied molecular orbital (HOMO and LUMO respectively) limited
effective interparticle coupling.

Physical size of band gap determines the photon’s emission
wavelength. Bandgap energy is inversely proportional to the square of the size
of the QD.

Quantum confinement effects: the bandgap (or HOMO-LUMO gap) of the
semiconductor nanocrystal increased with decreasing size, while discrete energy
levels arise at the band-edges. The energy separation between the band-edge
levels also increases with decreasing size. The colour of the luminescence
changes from red to blue as the QD diameter is reduced from 6 to 2nm.

 

Drummen, G., 2010: QD fluorescence: absorption of a photon higher in
energy than the spectral bandgap of the core semiconductor, resulting in
electron excitation to the conduction band, generating an electron-hole pair
(exciton).  Broad absorption spectrum
achieved due to long lifetime (10-40ns), as it increases the probability of
absorption at shorter wavelengths.

 

Energy-band structure is what gives the different electrical
characteristics in different materials. Electrons can move from the valence to
the conduction band, but only if they can satisfy that minimum amount of energy
that they require (either by absorbing a phonon -heat- or a photon -light-).

Temperature dependence of the energy bandgap

The energy bandgap of semiconductors tends to decrease as the
temperature is increased. This is because: the interatomic spacing increases
when the amplitude of the atomic vibrations increases due to the increased
thermal energy. This effect is quantified by the linear expansion coefficient
of a material. An increased interatomic spacing decreases the potential seen by
the electrons in the material, which in turn reduces the size of the energy
bandgap. A direct modulation of the interatomic distance, such as by applying
high compressive (tensile) stress, also causes an increase (decrease) of the
bandgap.

 

Quantum dots are semiconductor
nanocrystals varying in size from 2-10nm (10-50 atoms) in diameter. They
exhibit quantum mechanical effects allowing
them to mimic atomic properties. Bandgap
is the energy that they require for their electrons
to become excited. Small dot (blue) =
larger bandgap (i.e. electrons require a lot of energy to enter the excited state) Big dot (red) = smaller bandgap.
High energy = high frequency = small wavelength.