quantum dot

. Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic in nanotechnology and materials science. When a quantum dot is illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conduction band. The excited electron can drop back into the valence band releasing its energy as light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the discrete energy levels of the quantum dot in the conduction band and the valence band. In other words, a quantum dot can be defined as a structure on a semiconductor which is capable of confining electrons in three dimensions, enabling the ability to define discrete energy levels. The quantum dots are tiny crystals that can behave as individual atoms, and their properties can be manipulated. Nanoscale materials with semiconductor properties tightly confine either electrons or electron holes. The confinement is similar to a three-dimensional particle in a box model.…

. Quantum dots (QDs) or semiconductor nanocrystals are semiconductor particles a few nanometres in size with optical and electronic properties that differ from those of larger particles via quantum mechanical effects. They are a central topic in nanotechnology and materials science. When a quantum dot is illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conduction band. The excited electron can drop back into the valence band releasing its energy as light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the discrete energy levels of the quantum dot in the conduction band and the valence band. In other words, a quantum dot can be defined as a structure on a semiconductor which is capable of confining electrons in three dimensions, enabling the ability to define discrete energy levels. The quantum dots are tiny crystals that can behave as individual atoms, and their properties can be manipulated. Nanoscale materials with semiconductor properties tightly confine either electrons or electron holes. The confinement is similar to a three-dimensional particle in a box model. The quantum dot absorption and emission features correspond to transitions between discrete quantum mechanically allowed energy levels in the box that are reminiscent of atomic spectra. For these reasons, quantum dots are sometimes referred to as artificial atoms, emphasizing their bound and discrete electronic states, like naturally occurring atoms or molecules. It was shown that the electronic wave functions in quantum dots resemble the ones in real atoms. Quantum dots have properties intermediate between bulk semiconductors and discrete atoms or molecules. Their optoelectronic properties change as a function of both size and shape. Larger QDs of 5–6 nm diameter emit longer wavelengths, with colors such as orange, or red. Smaller QDs (2–3 nm) emit shorter wavelengths, yielding colors like blue and green. The specific emission energy of a QD depends on its dimensions, band gap energy, effective excited electron mass, and effective excited hole mass. Potential applications of quantum dots include single-electron transistors, solar cells, LEDs, lasers, single-photon sources, second-harmonic generation, quantum computing, cell biology research, microscopy, and medical imaging. Their small size allows for some QDs to be suspended in solution, which may lead to their use in inkjet printing, and spin coating. They have been used in Langmuir–Blodgett thin films. These processing techniques result in less expensive and less time-consuming methods of semiconductor fabrication. __TOC__ a^*_{\rm B}=\varepsilon_{\rm r}\left(\frac{m}{\mu}\right) a_{\rm B} where a B  = 0.053 nm is the Bohr radius, m is the mass, μ is the reduced mass, and ε r is the size-dependent dielectric constant (relative permittivity). 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. If the size distribution of QDs is not enough peaked, the convolution of multiple emission wavelengths is observed as a continuous spectra. 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 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 by Brus equation: \begin{align} E_\textrm{confinement} &= \frac{\hbar^2\pi^2}{2 a^2}\left(\frac{1}{m_{\rm e}} + \frac{1}{m_{\rm h}}\right) = \frac{\hbar^2\pi^2}{2\mu a^2}\\[6px] E_\textrm{exciton} &= -\frac{1}{\varepsilon_{\rm r}^2}\frac{\mu}{m_{\rm e}}R_y = -R_y^*\\[6px] 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, a is the radius of the quantum dot, m e is the free electron mass, m h is the hole mass, and ε r is the size-dependent dielectric constant. Although the above equations were derived using simplifying assumptions, they imply that the electronic transitions of the quantum dots will depend on their size. These quantum confinement effects are apparent only below the critical size. Larger particles do not exhibit this effect. This effect of quantum confinement on the quantum dots has been repeatedly verified experimentally and is a key feature of many emerging electronic structures. The Coulomb interaction between confined carriers can also be studied by numerical means when results unconstrained by asymptotic approximations are pursued. Besides confinement in all three dimensions (that is, 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. \mu(N) = E(N) - E(N-1) whose energy terms may be obtained as solutions of the Schrödinger equation. The definition of capacitance, \frac{1}{C} \equiv \frac{\Delta V}{\Delta Q} with the potential difference \Delta V = \frac{\Delta \mu}{e} = \frac{\mu(N+\Delta N) -\mu(N)}{e} may be applied to a quantum dot with the addition or removal of individual electrons, \Delta N = 1 \quad \text{and} \quad \Delta Q = e Then C(N) = \frac{e^2}{\mu(N+1)-\mu(N)} = \frac{e^2}{I(N)-A(N)} is the quantum capacitance of a quantum dot, where we denoted by the ionization potential and by the electron affinity of the N-particle system. Quantum dot on arxiv.org Quantum Dots Research and Technical Data Simulation and interactive visualization of Quantum Dots wave function

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