Section: B (2013-EE-88, 2013-EE-86, 2013-EE-90, 2013-EE-91)

Quantum Dots

Quantum dots are a nanoscale semiconductor devices. These crystals may contain

hundreds to thousands of atoms in it. And they are of various sizes depending on the number of

atoms and can be in different shapes. The size and shape of quantum dots gives them their

unique properties.

Each quantum dot depending on its size emits a particular wavelength of light. These

precision of wavelength is the key importance of quantum dots. This phenomenon can be

explained by quantum mechanics according to which electrons around the nucleus can only exist

in fixed orbits and not anywhere else.

Quantum dots were discovered in solids (glass crystals) in 1980 by Russian physicist Alexei

Ekimov while working at the Vavilov State Optical Institute. In late 1982, American chemist Louis

E. Brus, then working at Bell Laboratories (and now a professor at Columbia University),

discovered the same phenomenon in colloidal solutions (where small particles of one substance

are dispersed throughout another; milk is a familiar example). He discovered that the wavelength

of light emitted or absorbed by a quantum dot changed over a period of days as the crystal grew,

and concluded that the confinement of electrons was giving the particle quantum properties.

These two scientists shared the Optical Society of America's 2006 R.W. Wood Prize for their

pioneering work.

A quantum dot gets its name because it's a tiny speck of matter so small that it's

effectively concentrated into a single point (in other words, it's zero-dimensional). As a result,

the particles inside it that carry electricity (electrons and holes, which are places that are missing

electrons) are trapped ("constrained") and have well-defined energy levels according to the laws

of quantum theory (think rungs on a ladder), a bit like individual atoms. Tiny really does mean

tiny: quantum dots are crystals a few nanometers wide, so they're typically a few dozen atoms

across and contain anything from perhaps a hundred to a few thousand atoms. They're made

from a semiconductor such as silicon (a material that's neither really a conductor nor an insulator,

but can be chemically treated so it behaves like either). And although they're crystals, they

behave more like individual atoms—hence the nickname artificial atoms.

Quantum dots find various applications including brighter display for TVs to

medical imaging applications.

Quantum Mechanics and Quantum Dots

It is the theoretical basis of modern physics that explains the nature and behavior of

matter and energy on the atomic and subatomic level.

According to quantum mechanics electrons around a nucleus can only exist in quantized

orbitals and not anywhere else. And these orbits have particular amount of energy associated

with them. So whenever electron jumps from one orbit to another it has to emit or absorb that

particular amount to energy difference associated with those orbits.

Atoms emit or absorb energy in the form of photons. These are discrete packets of energy

and of different wavelength and energy. Greater the wave length lesser energy associated with

that photon and vice versa. Energy of a photon is given by:

𝐸 = ℎf

Where h is planks constant and f is frequency of emitted or absorbed photon.

Now when two or more atoms come together their energy orbitals interact with each

other and form energy bands. Now electron can only exist in those energy bands.

Max Planck:

Karl Ernst Ludwig Marx Planck, better known as Max, was born in Kiel in Holstein, northern

Germany on 23 April 1858. His family was traditional and intellectual (his father was a law

professor and his grandfather and great-grandfather had been theology professors). In 1867, the

family moved to Munich, where Planck attended the Ludwig Maximilians gymnasium school.

There, he came under the tutelage of Hermann Müller, who taught him astronomy and

mechanics as well as mathematics, and awoke Planck’s early interest in physics.He originated

quantum theory, which won him the Nobel Prize for Physics in 1918. In April 1885, the University

of Kiel appointed him as an associate professor of theoretical physics, and he continued to pursue

work on heat theory and on Rudolph Clausius’ ideas about entropy and its application in physical

chemistry.

In 1889, Planck moved to the University of Berlin, becoming a full professor in 1892.In

1894, Planck turned his attention to the problem of black body radiation,he investigated how the

intensity of the electromagnetic radiation emitted by a black body depends on the frequency of

the radiation (e.g. the colour of the light) and the temperature of the body.in 1899, he had noted

that the energy of photons could only take on certain discrete values which were always a full

integer multiple of a certain constant, which is now known as the “Planck constant”. Thus, light

and other waves were emitted in discrete packets of energy that he called "quanta".

Heisenberg:

Werner Heisenberg, in full Werner Karl Heisenberg (born December 5, 1901, Würzburg,

Germany—died February 1, 1976, Munich, West Germany), German physicist and philosopher

who discovered (1925) a way to formulate quantum mechanics in terms of matrices. For that

discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his

uncertainty principle, upon which he built his philosophy and for which he is best known. He also

made important contributions to the theories of the hydrodynamics of turbulent flows, the

atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles, and he was instrumental

in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor

in Munich, in 1957. Werner Heisenberg ranks alongside Niels Bohr, Paul Dirac and Richard

Feynman as far as his influence on contemporary physics is concerned. He was one of the most

important figures in the development of quantum mechanics, and its modern interpretation.

Heisenberg formulated the quantum theory of ferromagnetism, the neutron-proton

model of the nucleus, the S-matrix theory in particle scattering, and various other significant

breakthroughs in quantum field theory and high-energy particle physics are associated with him.

As a prolific author, Heisenberg wrote more than 600 original research papers, philosophical

essays and explanations for general audiences. His work is still available in the nine volumes of

the “Gesammelte Werke” (Collected Works).Heisenberg is synonymous with the so-called

uncertainty, or indeterminacy, principle of 1927, for one of the earliest breakthroughs to

quantum mechanics in 1925, and for his suggestion of a unified field theory, the so-called “world

formula”. He won the Nobel Prize for Physics in 1932 at the young age of 31.He also played a vital

role in the reconstruction of West German science after the war. Heisenberg’s role was crucial in

the success of West Germany’s nuclear and high-energy physics research programs.

(famousscientists.org)

Now here lies the key control over the specific light emitting phenomenon of quantum

dots. As the size of quantum dot increases there are more number of atoms in the crystal and

hence the energy band expands causing smaller gap between two energy bands. Therefore

energy difference is small. So the quantum dots with greater size emits light having larger

wavelength and quantum dots with smaller size emits light with smaller wavelength.

Synthesis techniques

They can be made via several possible routes including colloidal synthesis, plasma

synthesis, or mechanical fabrication. We discuss one method of synthesis a quantum dot CdSe.

1. First add Selenium and Octadecene in appropriate amounts and stirrer.

2. Then add Trioctylphosphine in appropriate amount in the solution and heat till it

forms clear liquid. What happens is that it forms trioctylphosphine selenide.

3. Then add cadmium oxide, Oleic Acid and Octadecene appropriate amounts and

stirrer and heat it forms cadmium oleate.

4. Then when temperature of Cadmium Oleate reaches at a particular point inject

trioctylphosphine selenide in it. And take samples from this solution after specific

intervals or when a change in color is observed.

These samples are quantum dots.

Size Control

The size of the nanocrystals can be easily controlled. While it is kept at constant

temperature it keeps on growing in size. And when we take it out of the solution in a test tube at

room temperature it looks its current size. By controlling this size of the quantum dot when can

control the color of light we want it to emit or absorb.

The first step in the growth of any sort of nanocrystal is

evidently the nucleation. Through a density fluctuation of the medium several atoms

assemble to a small crystal that is thermodynamically stable, and thus does not decay

to free atoms or ions. In that sense the nucleation can be understood as the overcoming of a

barrier. The nucleation in a solution at constant temperature and constant

pressure is driven by the difference in the free energy between the two phases. At the

simplest the driving forces in the nucleation event can be reduced to two, the gain in

the chemical potential and the increase of the total surface energy. The gain in

chemical potential can be understood as the energy freed by the formation of the

bonds in the growing crystal. The surface term takes into account the correction for

the incomplete saturation of the surface bonds. Upon formation of a spherical nucleus

consisting of n atoms the total free energy of the system changes by the value

∆𝐺 = 𝑛(𝜇𝑐 − 𝜇𝑠) + 4𝜋𝑟2𝜎

(𝜇c and 𝜇s are the chemical potentials of the crystalline phase and the solution phase,

respectively, r is the radius of the nucleus and 𝜎 the surface tension.)

Shape Control

Nanocrystals can be in various shapes. Not only spherical but they can be rod like

nanowires etc. Shape of these nanocrystals also gives them unique properties and so has various

applications.

The topic of size control is the foundation of modern reseach on colloidal

nanocrystals as we can synthesize any shape. In this field most of the current synthesis

techniques have been explored and developed. It has soon turned out that even small

variations of the standard synthesis schemes could lead to interesting effects, such as

the formation of nanocrystals with peculiar shapes. It is now possible to attain welldefined sizes

and shapes so that applications can be addressed. The attraction of the

field resides in the possibility to easily adjust the characteristics of the materials to a

desired value.

Basic Properties of Nanocrystals

Absorption: Absorption of photon by nanocrystal occurs if its energy exceeds from

the band gap. Due to quantum confinement decreasing the size results in blue shift.

Photoluminescence: The generation of luminance through photons is generally

divided into two categories florescence and phosphorescence, depending upon the

electronic configuration of the excited state and emission pathway. Florescence is the

ability of semiconductor to absorb energy greater than its band gap and after relaxation

photons to lowest exited state they emit light of higher wavelength than absorbed light.

The processes of phosphorescence occurs in similar manner.

Blinking Phenomenon: Spectroscopic investigation of single semiconductor NCs

revealed that their emission under continuous excitation turns on and off intermittently.

Applications of Quantum Dots

Quantum dots has many applications in daily life. They are so small that you can’t see

them with a typical microscope. In fact, they’re 10,000 times narrower than a human hair.

Quantum dots are actually very powerful devices and it’s their size that gives them a unique

ability: to convert light into nearly any color in the visible spectrum with very high efficiency.

Quantum dots display unique electronic properties, intermediate between those of bulk

semiconductors and discrete molecules, that are partly the result of the unusually high surface-

to-volume ratios for these particles .Due to their small size, the electrons in quantum dots are

confined in a small space (quantum box), and when the radii of the semiconductor nanocrystal is

smaller than the exciton Bohr radius, there is quantization of the energy levels according to

Pauli’s exclusion principle.

The discrete, quantized energy levels of quantum dots relate them more closely to atoms

than bulk materials and have resulted in quantum dots being nicknamed 'artificial atoms'.

Generally, as the size of the crystal decreases, the difference in energy between the highest

valence band and the lowest conduction band increases. More energy is then needed to excite

the dot, and concurrently, more energy is released when the crystal returns to its ground state,

resulting in a color shift from red to blue in the emitted light. As a result of this phenomenon,

quantum dots can emit any color of light from the same material simply by changing the dot size.

Additionally, because of the high level of control possible over the size of the nanocrystals

produced, quantum dots can be tuned during manufacturing to emit any color of light.

Because of these properties of QDs they have many applications. Following are some

interesting applications of quantum dots:

Quantum Display in TVs. As quantum dots are very selective in the

wavelength they emit. Therefore they are used in TV displays because they

give brighter and precise color with more efficiency and less power

consumption. QD improves the back light technology of TVs. In LCD TVs

the back light is simple white light. But as we know that white light isn’t

only red, green and blue. It has other colors too. And these other colors

need to be filtered before this light goes through as RGB pixels. And that

filtering will take away a little bit of light a little bit of vividness. But QD

back lighting doesn’t need that filtering. So it’ll shine pure red, blue and

green light through. And it’ll appear to be pure white but it won’t require

any filtering. So it’ll produce a much brighter image.

So far, quantum dots have attracted most interest because of their interesting optical

properties: they're being used for all sorts of applications where precise control of colored light

is important. In one simple and relatively trivial application, a thin filter made of quantum dots

has been developed so it can be fitted on top of a fluorescent or LED lamp and convert its light

from a blueish color to a warmer, redder, more attractive shade similar to the light produced by

old-fashioned incandescent lamps. Quantum dots can also be used instead of pigments and dyes.

Embedded in other materials, they absorb incoming light of one color and give out light of an

entirely different color; they're brighter and more controllable than organic dyes (artificial dyes

made from synthetic chemicals).The quantum dots have electron energy states that can be tuned

to precise colours, such as the rich reds and greens needed for TVs. Excited by the high intensity

blue-white LEDs commonly used in backlights, the dots produce brightly coloured light with a

very narrow spectral profile.

Quantum Dots also find their applications in solar cells. We can extract

more energy by using solar cells made up of quantum dots than using

conventional solar cells because we can design the quantum dots such that

they absorb the most part of the energy spectrum than a conventional

solar would. QDs helps to absorb as much light as possible. We design the

QDs such that they absorb most of the spectrum energy coming from sun.

And hence increases efficiency. In a traditional solar cell, photons of

sunlight knock electrons out of a semiconductor into a circuit, making

useful electric power, but the efficiency of the process is quite low.

Quantum dots produce more electrons (or holes) for each photon that

strikes them, potentially offering a boost in efficiency of perhaps 10

percent over conventional semiconductors. CCDs (charge-coupled

devices), which are the image-detecting chips in such things as digital

cameras and webcams, work in a similar way to solar cells, by converting

incoming light into patterns of electrical signals; efficient quantum dots

could be used to make smaller and more efficient CCDs for applications

where conventional devices are too big and clumsy.

Quantum Dots are used for producing better images in medical

applications. Imaging of cellular and subcellular structure and functional

cell imaging in live animals in real time. But their safety is under study yet.

Quantum dots are also finding important medical applications, including

potential cancer treatments. Dots can be designed so they accumulate in

particular parts of the body and then deliver anti-cancer drugs bound to

them. Their big advantage is that they can be targeted at single organs,

such as the liver, much more precisely than conventional drugs, so

reducing the unpleasant side effects that are characteristic of untargeted,

traditional chemotherapy. Quantum dots are also being used in place of

organic dyes in biological research; for example, they can be used like

nanoscopic light bulbs to light up and color specific cells that need to be

studied under a microscope. They're also being tested as sensors for

chemical and biological warfare agents such as anthrax. Unlike organic

dyes, which operate over a limited range of colors and degrade relatively

quickly, quantum dyes are very bright, can be made to produce any color

of visible light, and theoretically last indefinitely (they are said to be

photostable).

Quantum computers are the new emerging technology. They are under

research now. They work on the principles of quantum physics. The unit of

information in them is qubit. Quantum dots are used as qubit in quantum

computers. These computers decreases the number of steps required for

a particular task significantly as compared to classical computers.

A Qubit can store more information than classical bit. According to

quantum mechanics tiny particles can exit in all possible states

simultaneous unless their state is determined. Because of this we can store

enormous amount of data in Qubits. As shown in figure arrow represents

the state of the Qubit. Arrow pointing in any direction gives different state.

We can so represent information by this rather than only two options 0

and 1 which we have in classical computers. But information handling in

Qubits is tricky business. Because we may not want to know the exact sate

of the Qubit because if we do so then the Qubit would stop existing in all

states simultaneously but rather exist in one of all those possible states.