# Quantum dot

Colloidal quantum dots irradiated with a UV light. Different sized quantum dots emit different color light due to quantum confinement.

A quantum dot is a portion of matter (e.g., semiconductor) whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules.[1][2][3] They were discovered at the beginning of the 1980s by Alexei Ekimov[4] in a glass matrix and by Louis E. Brus in colloidal solutions. The term "quantum dot" was coined by Mark Reed.[5]

Researchers have studied quantum dots in transistors, solar cells, LEDs, and diode lasers. They have also investigated quantum dots as agents for medical imaging and hope to use them as qubits in quantum computing.

Stated simply, quantum dots are semiconductors whose electronic characteristics are closely related to the size and shape of the individual crystal. Generally, the smaller the size of the crystal, the larger the band gap, the greater the difference in energy between the highest valence band and the lowest conduction band becomes, therefore more energy is needed to excite the dot, and concurrently, more energy is released when the crystal returns to its resting state. For example, in fluorescent dye applications, this equates to higher frequencies of light emitted after excitation of the dot as the crystal shrinks to smaller sizes, resulting in a color shift from red to blue in the light emitted. In addition to such tuning, a main advantage with quantum dots is that, because of the high level of control possible over the size of the crystals produced, it is possible to have very precise control over the conductive properties of the material.[6] Quantum dots of different sizes can be assembled into a gradient multi-layer nanofilm.

## Quantum confinement in semiconductors

3D confined electron wave functions in a quantum dot. Here, rectangular and triangular-shaped quantum dots are shown. Energy states in rectangular dots are more s-type and p-type. However, in a triangular dot the wave functions are mixed due to confinement symmetry. (Click for animation)

In a semiconductor crystallite smaller than the characteristic size of the exciton determined by the Coulomb attraction (the exciton Bohr radius), the excitons are squeezed, leading to quantum confinement. The energy levels can then be modeled using particle in a box, which leads to size-dependence of the exciton energy. The exciton Bohr radius is larger than the regular hydrogenic Bohr radius due to the effect of dielectric screening and the influence of periodic lattice structure of the crystal. The quantum dots that have radii of the order of the exciton Bohr radius are said to be in the 'weak confinement regime' and the ones that have radii smaller than the exciton Bohr radius are said to be in the 'strong confinement regime'. Thus, if the size of the quantum dot is small enough that the quantum confinement effects dominate (typically less than 10 nm), the electronic and optical properties change, like the fluorescent wavelength which is determined by the size.

Splitting of energy levels for small quantum dots due to the quantum confinement effect. The horizontal axis is the radius, or the size, of the quantum dots and ab* is the Exciton Bohr radius.

The fluorescence of the quantum dots is a result of exciting the valence electron with a certain energy(or wavelength) and the emission of lower energy in the form of photons as the excited electron returns to the ground state, combining with the hole. The energy of the emitted photon is determined by the size of the quantum dot due to quantum confinement effects. In a simplified model of the excitation, the energy of the emitted photon can be seen as a sum of the band gap energy between occupied level and unoccupied energy level, the confinement energies of the hole and the excited electron, and the bound energy of the exciton (the electron-hole pair):

Band gap energy
The band gap can become larger in the strong confinement regime where the size of the quantum dot is smaller than the Exciton Bohr radius (ab* in the figure) as the energy levels split up.
where ab is the Bohr radius=0.053 nm, m is the mass, μ is the reduced mass, and εr is the size-dependent dielectric constant
This results in the increase in the total emission energy (the sum of the energy levels in the smaller band gaps in the strong confinement regime is larger than the energy levels in the band gaps of the original levels in the weak confinement regime) and the emission at various wavelengths; which is precisely what happens in the sun, where the quantum confinement effects are completely dominant and the energy levels split up to the degree that the energy spectrum is almost continuous, thus emitting white light.
Confinement energy
The exciton entity can be modeled using the particle in the box. The electron and the hole can be seen as hydrogen in the Bohr model with the hydrogen nucleus replaced by the hole of positive charge and negative electron mass. Then the energy levels of the exciton can be represented as the solution to the particle in a box at the ground level (n = 1) with the mass replaced by the reduced mass. Thus by varying the size of the quantum dot, the confinement energy of the exciton can be controlled.
Bound exciton energy
There is Coulomb attraction between the negatively charged electron and the positively charged hole. The negative energy involved in the attraction is proportional to Rydberg's energy and inversely proportional to square of the size-dependent dielectric constant[7] of the semiconductor. When the size of the semiconductor crystal is smaller than the Exciton Bohr radius, the Coulomb interaction must be modified to fit the situation.

Therefore, the sum of these energies can be represented as:

\begin{align} E_\textrm{confinement} &= \frac{\hbar^2\pi^2}{2 a^2}\left(\frac{1}{m_e} + \frac{1}{m_h}\right) = \frac{\hbar^2\pi^2}{2\mu a^2}\\ E_\textrm{exciton} &= -\frac{1}{\epsilon_r^2}\frac{\mu}{m_e}R_y = -R_y^*\\ E &= E_\textrm{band gap} + E_\textrm{confinement} + E_\textrm{exciton}\\ &= E_\textrm{band gap} + \frac{\hbar^2\pi^2}{2\mu a^2} - R^*_y \end{align}

where:

• μ is the reduced mass
• me is the free electron mass
• mh is the hole mass
• εr is the size-dependent dielectric constant

Although the above equations were derived using simplifying assumptions, the implications are clear; the energy of the quantum dots are dependent on their size due to the quantum confinement effects, which dominate below the critical size leading to changes in the optical properties. This effect of quantum confinement on the quantum dots have been experimentally verified[8] and is a key feature of many emerging electronic structures.[9][10]

Besides confinement in all three dimensions (i.e., a quantum dot), other quantum confined semiconductors include:

• Quantum wires, which confine electrons or holes in two spatial dimensions and allow free propagation in the third.
• Quantum wells, which confine electrons or holes in one dimension and allow free propagation in two dimensions.

## Production

There are several ways to confine excitons in semiconductors, resulting in different methods to produce quantum dots. In general, quantum wires, wells and dots are grown by advanced epitaxial techniques in nanocrystals produced by chemical methods or by ion implantation, or in nanodevices made by state-of-the-art lithographic techniques.[11]

### Colloidal synthesis

Colloidal semiconductor nanocrystals are synthesized from precursor compounds dissolved in solutions, much like traditional chemical processes. The synthesis of colloidal quantum dots is based on a three-component system composed of precursors, organic surfactants, and solvents. When heating a reaction medium to a sufficiently high temperature, the precursors chemically transform into monomers. Once the monomers reach a high enough supersaturation level, the nanocrystal growth starts with a nucleation process. The temperature during the growth process is one of the critical factors in determining optimal conditions for the nanocrystal growth. It must be high enough to allow for rearrangement and annealing of atoms during the synthesis process while being low enough to promote crystal growth. Another critical factor that has to be stringently controlled during nanocrystal growth is the monomer concentration. The growth process of nanocrystals can occur in two different regimes, "focusing" and "defocusing". At high monomer concentrations, the critical size (the size where nanocrystals neither grow nor shrink) is relatively small, resulting in growth of nearly all particles. In this regime, smaller particles grow faster than large ones (since larger crystals need more atoms to grow than small crystals) resulting in "focusing" of the size distribution to yield nearly monodisperse particles. The size focusing is optimal when the monomer concentration is kept such that the average nanocrystal size present is always slightly larger than the critical size. When the monomer concentration is depleted during growth, the critical size becomes larger than the average size present, and the distribution "defocuses" as a result of Ostwald ripening.

There are colloidal methods to produce many different semiconductors. Typical dots are made of binary alloys such as cadmium selenide, cadmium sulfide, indium arsenide, and indium phosphide. Dots may also be made from ternary alloys such as cadmium selenide sulfide. These quantum dots can contain as few as 100 to 100,000 atoms within the quantum dot volume, with a diameter of 10 to 50 atoms. This corresponds to about 2 to 10 nanometers, and at 10 nm in diameter, nearly 3 million quantum dots could be lined up end to end and fit within the width of a human thumb.

Large batches of quantum dots may be synthesized via colloidal synthesis. Due to this scalability and the convenience of benchtop conditions, colloidal synthetic methods are promising for commercial applications. It is acknowledged[citation needed] to be the least toxic of all the different forms of synthesis.

### Fabrication

• Self-assembled quantum dots are typically between 5 and 50 nm in size. Quantum dots defined by lithographically patterned gate electrodes, or by etching on two-dimensional electron gases in semiconductor heterostructures can have lateral dimensions exceeding 100 nm.
• Some quantum dots are small regions of one material buried in another with a larger band gap. These can be so-called core–shell structures, e.g., with CdSe in the core and ZnS in the shell or from special forms of silica called ormosil.
• Quantum dots sometimes occur spontaneously in quantum well structures due to monolayer fluctuations in the well's thickness.
• Self-assembled quantum dots nucleate spontaneously under certain conditions during molecular beam epitaxy (MBE) and metallorganic vapor phase epitaxy (MOVPE), when a material is grown on a substrate to which it is not lattice matched. The resulting strain produces coherently strained islands on top of a two-dimensional wetting layer. This growth mode is known as Stranski–Krastanov growth. The islands can be subsequently buried to form the quantum dot. This fabrication method has potential for applications in quantum cryptography (i.e. single photon sources) and quantum computation. The main limitations of this method are the cost of fabrication and the lack of control over positioning of individual dots.
• Individual quantum dots can be created from two-dimensional electron or hole gases present in remotely doped quantum wells or semiconductor heterostructures called lateral quantum dots. The sample surface is coated with a thin layer of resist. A lateral pattern is then defined in the resist by electron beam lithography. This pattern can then be transferred to the electron or hole gas by etching, or by depositing metal electrodes (lift-off process) that allow the application of external voltages between the electron gas and the electrodes. Such quantum dots are mainly of interest for experiments and applications involving electron or hole transport, i.e., an electrical current.
• The energy spectrum of a quantum dot can be engineered by controlling the geometrical size, shape, and the strength of the confinement potential. Also, in contrast to atoms, it is relatively easy to connect quantum dots by tunnel barriers to conducting leads, which allows the application of the techniques of tunneling spectroscopy for their investigation.

The quantum dot absorption features correspond to transitions between discrete,three-dimensional particle in a box states of the electron and the hole, both confined to the same nanometer-size box.These discrete transitions are reminiscent of atomic spectra and have resulted in quantum dots also being called artificial atoms.[12]

• Confinement in quantum dots can also arise from electrostatic potentials (generated by external electrodes, doping, strain, or impurities).
• CMOS technology can be employed to fabricate silicon quantum dots. Ultra small (L=20 nm, W=20 nm) CMOS transistors behave as single electron quantum dots when operated at cryogenic temperature over a range of −269 °C (4 K) to about −258 °C (15 K). The transistor displays Coulomb blockade due to progressive charging of electrons one by one. The number of electrons confined in the channel is driven by the gate voltage, starting from an occupation of zero electrons, and it can be set to 1 or many.[13]

### Viral assembly

Lee et al. (2002) reported using genetically engineered M13 bacteriophage viruses to create quantum dot biocomposite structures.[14] As a background to this work, it has previously been shown that genetically engineered viruses can recognize specific semiconductor surfaces through the method of selection by combinatorial phage display.[15] Additionally, it is known that liquid crystalline structures of wild-type viruses (Fd, M13, and TMV) are adjustable by controlling the solution concentrations, solution ionic strength, and the external magnetic field applied to the solutions. Consequently, the specific recognition properties of the virus can be used to organize inorganic nanocrystals, forming ordered arrays over the length scale defined by liquid crystal formation. Using this information, Lee et al. (2000) were able to create self-assembled, highly oriented, self-supporting films from a phage and ZnS precursor solution. This system allowed them to vary both the length of bacteriophage and the type of inorganic material through genetic modification and selection.

### Electrochemical assembly

Highly ordered arrays of quantum dots may also be self-assembled by electrochemical techniques. A template is created by causing an ionic reaction at an electrolyte-metal interface which results in the spontaneous assembly of nanostructures, including quantum dots, onto the metal which is then used as a mask for mesa-etching these nanostructures on a chosen substrate.

### Bulk-manufacture

Quantum dot manufacturing relies on a process called "high temperature dual injection" which has been scaled by multiple companies for commercial applications that require large quantities (100's of kgs to tonnes) of quantum dots. This is a reproducible production method that can be applied to a wide range of quantum dot sizes and compositions.

An alternative method that has been reported for creating large quantities quantum dots involves producing nanoparticles from chemical precursors in the presence of a molecular cluster compound under conditions whereby the integrity of the molecular cluster is maintained and acts as a prefabricated seed template. Individual molecules of a cluster compound act as a seed or nucleation point upon which nanoparticle growth can be initiated. In this way, a high temperature nucleation step is not necessary to initiate nanoparticle growth because suitable nucleation sites are already provided in the system by the molecular clusters. A significant disadvantage of this method is that it requires the additional step of synthesizing the molecular cluster, and that the growth typically takes days or even a week, versus the high temperature injection method which can form quantum dots in an hour or less.

Recently a consortium of U.S. and Dutch companies reported a "milestone" in high volume quantum dot manufacturing by applying the traditional high temperature dual injection method to a flow system.[16] However as of 2011, applications using bulk-manufactured quantum dots are scarcely available.[17]

Cadmium-free quantum dots are also called "CFQD". In many regions of the world there is now a restriction or ban on the use of heavy metals in many household goods which means that most cadmium based quantum dots are unusable for consumer-goods applications.

For commercial viability, a range of restricted, heavy metal-free quantum dots has been developed showing bright emissions in the visible and near infra-red region of the spectrum and have similar optical properties to those of CdSe quantum dots.

Cadmium and other restricted heavy metals used in conventional quantum dots is of a major concern in commercial applications. For Quantum Dots to be commercially viable in many applications they must not contain cadmium or other restricted metal elements.[18]

A new type of CFQD can be made from rare earth (RE) doped oxide colloidal phosphor nanoparticles.[19] Unlike semiconductor nanoparticles, excitation was due to UV absorption of host material, which is same for different RE doped materials using same host. Multiplexing applications can be thus realized. The emission depends on the type of RE, which enables very large stokes shift and is narrower than CdSe QDs. The synthesis is aqueous based, which eliminated issues of water solubility for biological applications. The oxide surface might be easier for chemical functionalization more and chemically stable in various environments. Some reports exist concerning the use of such phosphor nanoparticles on biological targeting and imaging.[20]

## Optical properties

Fluorescence spectra of CdTe quantum dots of various sizes. Different sized quantum dots emit different color light due to quantum confinement.

An immediate optical feature of colloidal quantum dots is their color. While the material which makes up a quantum dot defines its intrinsic energy signature, the nanocrystal's quantum confined size is more significant at energies near the band gap. Thus quantum dots of the same material, but with different sizes, can emit light of different colors. The physical reason is the quantum confinement effect.

The larger the dot, the redder (lower energy) its fluorescence spectrum. Conversely, smaller dots emit bluer (higher energy) light. The coloration is directly related to the energy levels of the quantum dot. Quantitatively speaking, the bandgap energy that determines the energy (and hence color) of the fluorescent light is inversely proportional to the size of the quantum dot. Larger quantum dots have more energy levels which are also more closely spaced. This allows the quantum dot to absorb photons containing less energy, i.e., those closer to the red end of the spectrum. Recent articles in Nanotechnology and in other journals have begun to suggest that the shape of the quantum dot may be a factor in the coloration as well, but as yet not enough information is available. Furthermore, it was shown [21] that the lifetime of fluorescence is determined by the size of the quantum dot. Larger dots have more closely spaced energy levels in which the electron-hole pair can be trapped. Therefore, electron-hole pairs in larger dots live longer causing larger dots to show a longer lifetime.

As with any crystalline semiconductor, a quantum dot's electronic wave functions extend over the crystal lattice. Similar to a molecule, a quantum dot has both a quantized energy spectrum and a quantized density of electronic states near the edge of the band gap.

Qdots can be synthesized with larger (thicker) shells (CdSe qdots with CdS shells). The shell thickness has shown direct correlation to the spectroscopic properties of the particles like lifetime and emission intensity, but also to the stability.

## Applications

Quantum dots are particularly significant for optical applications due to their high extinction coefficient.[22] In electronic applications they have been proven to operate like a single electron transistor and show the Coulomb blockade effect. Quantum dots have also been suggested as implementations of qubits for quantum information processing.

The ability to tune the size of quantum dots is advantageous for many applications. For instance, larger quantum dots have a greater spectrum-shift towards red compared to smaller dots, and exhibit less pronounced quantum properties. Conversely, the smaller particles allow one to take advantage of more subtle quantum effects.

Researchers at Los Alamos National Laboratory have developed a wireless device that efficiently produces visible light, through energy transfer from thin layers of quantum wells to crystals above the layers.

Being zero dimensional, quantum dots have a sharper density of states than higher-dimensional structures. As a result, they have superior transport and optical properties, and are being researched for use in diode lasers, amplifiers, and biological sensors. Quantum dots may be excited within a locally enhanced electromagnetic field produced by gold nanoparticles, which can then be observed from the surface plasmon resonance in the photoluminescent excitation spectrum of (CdSe)ZnS nanocrystals. High-quality quantum dots are well suited for optical encoding and multiplexing applications due to their broad excitation profiles and narrow/symmetric emission spectra. The new generations of quantum dots have far-reaching potential for the study of intracellular processes at the single-molecule level, high-resolution cellular imaging, long-term in vivo observation of cell trafficking, tumor targeting, and diagnostics.

### Computing

Quantum dot technology is one of the most promising candidates for use in solid-state quantum computation. By applying small voltages to the leads, the flow of electrons through the quantum dot can be controlled and thereby precise measurements of the spin and other properties therein can be made. With several entangled quantum dots, or qubits, plus a way of performing operations, quantum calculations and the computers that would perform them might be possible.

### Biology

In modern biological analysis, various kinds of organic dyes are used. However, with each passing year, more flexibility is being required of these dyes, and the traditional dyes are often unable to meet the expectations.[23] To this end, quantum dots have quickly filled in the role, being found to be superior to traditional organic dyes on several counts, one of the most immediately obvious being brightness (owing to the high extinction co-efficient combined with a comparable quantum yield to fluorescent dyes [24]) as well as their stability (allowing much less photobleaching). It has been estimated that quantum dots are 20 times brighter and 100 times more stable than traditional fluorescent reporters.[23] For single-particle tracking, the irregular blinking of quantum dots is a minor drawback.

The usage of quantum dots for highly sensitive cellular imaging has seen major advances over the past decade. The improved photostability of quantum dots, for example, allows the acquisition of many consecutive focal-plane images that can be reconstructed into a high-resolution three-dimensional image.[25] Another application that takes advantage of the extraordinary photostability of quantum dot probes is the real-time tracking of molecules and cells over extended periods of time.[26] Antibodies, streptavidin,[27] peptides,[28] nucleic acid aptamers,[29] or small-molecule ligands can be used to target quantum dots to specific proteins on cells. Researchers were able to observe quantum dots in lymph nodes of mice for more than 4 months.[30]

Semiconductor quantum dots have also been employed for in vitro imaging of pre-labeled cells. The ability to image single-cell migration in real time is expected to be important to several research areas such as embryogenesis, cancer metastasis, stem cell therapeutics, and lymphocyte immunology.

Scientists have proven that quantum dots are dramatically better than existing methods for delivering a gene-silencing tool, known as siRNA, into cells.[31]

First attempts have been made to use quantum dots for tumor targeting under in vivo conditions. There exist two basic targeting schemes: active targeting and passive targeting. In the case of active targeting, quantum dots are functionalized with tumor-specific binding sites to selectively bind to tumor cells. Passive targeting uses the enhanced permeation and retention of tumor cells for the delivery of quantum dot probes. Fast-growing tumor cells typically have more permeable membranes than healthy cells, allowing the leakage of small nanoparticles into the cell body. Moreover, tumor cells lack an effective lymphatic drainage system, which leads to subsequent nanoparticle-accumulation.

One of the remaining issues with quantum dot probes is their potential in vivo toxicity. For example, CdSe nanocrystals are highly toxic to cultured cells under UV illumination. The energy of UV irradiation is close to that of the covalent chemical bond energy of CdSe nanocrystals. As a result, semiconductor particles can be dissolved, in a process known as photolysis, to release toxic cadmium ions into the culture medium. In the absence of UV irradiation, however, quantum dots with a stable polymer coating have been found to be essentially nontoxic.[30][32] Then again, only little is known about the excretion process of quantum dots from living organisms.[33] These and other questions must be carefully examined before quantum dot applications in tumor or vascular imaging can be approved for human clinical use.

Another potential cutting-edge application of quantum dots is being researched, with quantum dots acting as the inorganic fluorophore for intra-operative detection of tumors using fluorescence spectroscopy.

### Photovoltaic devices

Quantum dots may be able to increase the efficiency and reduce the cost of today's typical silicon photovoltaic cells. According to an experimental proof from 2006 (controversial results[34]), quantum dots of lead selenide can produce as many as seven excitons from one high energy photon of sunlight (7.8 times the bandgap energy).[35] This compares favorably to today's photovoltaic cells which can only manage one exciton per high-energy photon, with high kinetic energy carriers losing their energy as heat. This would not result in a 7-fold increase in final output however, but could boost the maximum theoretical efficiency from 31% to 42%. Quantum dot photovoltaics would theoretically be cheaper to manufacture, as they can be made "using simple chemical reactions."[35] The generation of more than one exciton by a single photon is called multiple exciton generation (MEG) or carrier multiplication.

### Light emitting devices

There are several inquiries into using quantum dots as light-emitting diodes to make displays and other light sources, such as "QD-LED" displays, and "QD-WLED" (White LED). In June, 2006, QD Vision announced technical success in making a proof-of-concept quantum dot display and show a bright emission in the visible and near infra-red region of the spectrum. Quantum dots are valued for displays, because they emit light in very specific gaussian distributions. This can result in a display that more accurately renders the colors that the human eye can perceive. Quantum dots also require very little power since they are not color filtered. Additionally, since the discovery of "white-light emitting" QD, general solid-state lighting applications appear closer than ever.[36] A color liquid crystal display (LCD), for example, is usually powered by a single fluorescent lamp (or occasionally, conventional white LEDs) that is color filtered to produce red, green, and blue pixels. Displays that intrinsically produce monochromatic light can be more efficient, since more of the light produced reaches the eye.QD-LEDs can be fabricated on a silicon substrate, which allows integration of light sources onto silicon-based integrated circuits or microelectromechanical systems.[37] A QD-LED integrated at a scanning microscopy tip was used to demonstrate fluorescence near-field scanning optical microscopy (NSOM) imaging.[38]

### Photodetector devices

Quantum dot photodetectors (QDPs) can be fabricated either via solution-processing,[39] or from conventional single-crystalline semiconductors.[40] Conventional single-crystalline semiconductor QDPs are precluded from integration with flexible organic electronics due to the incompatibility of their growth conditions with the process windows required by organic semiconductors. On the other hand, solution-processed QDPs can be readily integrated with an almost infinite variety of substrates, and also postprocessed atop other integrated circuits. Such colloidal QDPs have potential applications in surveillance, machine vision, industrial inspection, spectroscopy, and fluorescent biomedical imaging.

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