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Rajkiran
Quantum dots and Quantum wells 

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Introduction This presentation covers three main topics:
Quantum confinement: overview.
Quantum dots : theory, synthesis ,and applications.
Quantum wells: overview.



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Band gap Schematic plot of the single particle
energy band gap. The upper parabolic band
is the conduction band, the lower the
valence. 

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Quantum dots are in range of 4 to 10 nanometers.
Anything below one nanometers is considered as molecular state and ions.
Bulk can vary from microns to any large quantity.
Nanoparticles can range from 1 to 100 nanometers .
bulk
quantum dots
molecules
nanoparticles 

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QUANTUM CONFINEMENT QUANTUM CONFINEMENT IS MOSTLY STUDIED IN MATERIAL CALLED QUANTUM DOTS.
CONFINEMENT LITRALLY MEANS RESTRICTING SOMETHING TO SOME RESOURCE.
IN QUNATUM CONFINEMENT WE RESTRICT ELECTRON OR EXITON TO SPACE.
WE SYNTHESIZE NANOPARTICALS WHICH ARE IN NANO DIMENTIONS.
THE WAVELENGHT OF ELECTRON IS ALSO IN THE DIMENTIONS OF NANOMETERS, SO A ELECTRON FEELS CONFINED IN THE SPACE.
AT THIS DIMENTIONS THE QUANTUMSIZE EFFECTS COME INTO VIEW.
THERE ARE DIFFERENT TYPES OF CONFINMENTS.


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In semiconductors when a electron is exited from valence band to conduction band an particle analogous to positronium called exciton is formed.
Exciton is a bound pair of electron and proton.
The particle exciton has a radius equal to :
a=h^2/4?^2e^2[1/m (e)+1/m(h)] E=dielectric constant e= elementary charge
quantum size effects manifested when d˜a.
d= diameter of quantum dot
It is 56 A ° for cdse. QUANTUM CONFINEMENT 


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Quantum confinement 3D
All carriers act as free carriers in all three directions
2D or Quantum Wells
The carriers act as free carriers in a plane
First observed in semiconductor systems
1D or Quantum Wires
The carriers are free to move down the direction of the wire
0D or Quantum Dots
Systems in which carriers are confined in all directions (no free carriers) 



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Discovery
Quantum dots were first discovered by ALEXI EKIMOV in glass matrix.
The name quantum dot was coined by MARK REED. 

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Quantum dots are semiconductors that are on the nanometer scale(4 to 10 nm for quantum dots)
Obey quantum mechanical principle of quantum confinement.
Exhibit energy band gap that determines required wavelength of radiation absorption and emission spectra.
Requisite absorption and resultant emission wavelengths
dependent on dot size
Quantum dots introduction 

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Quantum dots Allowed bound eh states can be calculated by solving the Schrödinger equation
for particles (electrons and holes) with effective mass mi*, as well as a
mutual interaction potential given by the interparticle spacing . Here e is the dielectric constant of the material
This results in a minimum radius of the bound eh pair which is the exciton Bohr radius, with µ the effective mass of the exciton 

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Quantum dot
Material Dependent Parameter
The same size dot of different materials may not both be quantum dots
The Bohr Diameter determines the type of confinement
310 time Bohr Diameter: Weak Confinement
?E ~ 1/M*
M* effective mass of exciton
Smaller than 3 Bohr Diameter: Strong Confinement
?E ~ 1/µ*
µ* effective mass of hole and electron 

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Synthesis of quantum dots This method involves synthesis of nano particles through chemical route.
The synthesis is through precursor mediated method.
Selenium precursor and cadmium precursor are used in this preparations of quantum dots.
A organic solvent having high boiling point is used which is octadecene.
the cadmium solution with capping agent like tetraoctylphosphine is boiled to higher temperatures.
Then the selenium solution is added.
The nucleation followed by growth and ostwald ripening is carried on. 

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The samples from reaction mixture are removed quickly in in different intervals of time.
A mere glance at samples obtained itself gives us about the absorption properties about qd’s.
The uv spectroscopy gives us information about the absorption of different size nanoparticals. 

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Size related optical properties Quantum dots show different properties that vary with their particle properties.
Qd’s show different absorption spectra that differ with other qd’s of different sizes.
As the size of quantum dots increases the colour of quantum dots changes and sifts to red .
The absorption shifts to blue range as the particle size increases.
In other words the bigger particle absorbs higher energy with shorter wave length(blue shift). 

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Applications Photovoltaic devices: solar cells
Biology : biosensors, imaging
Light emitting diodes: LEDs
Quantum computation
Flatpanel displays
Memory elements
Photodetectors
Lasers 

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Quantum dots in imagining 


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Quantum wells There are different types of quantum confinements .
If electrons are confined in only one dimensions and free other two dimensions then this type of confinement forms the quantum wells.
If electrons are confined in three dimensions then this type of confinement forms the quantum dots.
Quantum dots are called zero dimensional nanomaterial structures because they are confined in all three dimensions.
Quantum wells are called two dimensional nanomaterial because they are confined in all one dimensions.


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quantum wells The concept of two dimensional quantum wells can be explained by imagining it as a thin films .
In thin film the length and breath are in large but the thickness of the film is comparatively small .
Likewise the electron is confined in a thin film whose thickness in the dimensions of nanometers.
That’s why sometimes quantum wells are considered as quantum films.
electrons feel a potential well as trapped in the film.
In two dimensional confinement electrons are confined in 2d area. 

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quantum wells Sometimes it is considered that quantum dots grow or assemble into form quantum wells.
Any nanocrystals have density of states which are different from their bulk material.
quantum dots have density of states which are discrete and they are over large band spaces.
Quantum wells have steplike density of states. 

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Quantum wells Thin film of quantum well Density of states of quantum wells 

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Density of states in various dimensions 

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Potential well A potential well is the region surrounding a local minimum of potential energy.
Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy.
The graph of a 2D potential energy function is a potential energy surface that can be imagined as the Earth's surface in a landscape of hills and valleys. Then a potential well would be a valley surrounded on all sides with higher terrain, which thus could be filled with water (i.e., be a lake) without any water flowing away toward another, lower minimum (i.e. sea level). 

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Quantum wells A quantum well is a potential well that confines particles, which were originally free to move in three dimensions, to two dimensions, forcing them to occupy a planar region. The effects of quantum confinement take place when the quantum well thickness becomes comparable at the de Broglie wavelength of the carriers (generally electrons and holes).
Quantum wells are formed in semiconductors by having a material, like gallium arsenide sandwiched between two layers of a material with a wider bandgap, like aluminium arsenide.


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Thin film semiconductors Electrons in conduction band (and holes in the valence band) are free to move in two dimensions.
Confined in one dimension by a potential well.
Potential well created due to a larger bandgap of the semiconductors on either side of the thin film.
Thinner films lead to higher energy levels. 

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Quantum wells Quantum well is a “sandwich” made of two different semiconductors in which the energy of the electrons is different, and whose atomic spacing's are so similar that they can be grown together without an appreciable density of defects:


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Quantum wells Quantum wells are covered with a polymer mask and exposed to an electron or ion beam.
The surface is covered with a thin layer of metal, then cleaned and only the exposed areas keep the metal layer.
Pillars are etched into the entire surface.
Multiple layers are applied this way to build up the properties and size wanted.
Disadvantages: slow, contamination, low density, defect formation. 

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summary The concept of quantum dots and quantum wells are explained with the phenomenon of quantum confinement.
Quantum dots and quantum wells as we have seen are mostly semiconducting materials.
There are many potential applications that can be achieved by using these nanomaterials.


