quantum dot

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A quantum dot is a semiconductor nanocrystal typically 2 to 10 nm in size, in which the motion of charge carriers (electrons and holes) is confined in all three dimensions, leading to quantization of the energy spectrum. Due to spatial confinement, energy levels become discrete, like atomic ones, and depend on the dot's size. Optical transitions between these levels yield narrow luminescence bands. The emission color can be continuously tuned by changing the nanocrystal diameter.

History

The first quantum dots were accidentally created by Russian scientist Alexey Ekimov in 1981 while growing nanocrystals in glass. In 1984, Louis Brus from the USA explained their unusual optical properties and introduced the term 'quantum confinement'. Later, Moungi Bawendi developed a method for synthesizing monodisperse dots suitable for mass production.

How it works

An electron in a quantum dot is like a ball in a small sandbox with high edges. Its freedom of movement is restricted, and it can only occupy discrete positions. Similarly in a quantum dot: due to the tiny size, only certain allowed orbits are available to the electron. When it 'jumps' from one orbit to another, energy is released in the form of a photon of a very specific wavelength.

💡 Quantum dots are so bright and stable that they are used to create TVs with record color gamut, and in biology to track the movement of a single molecule inside a living cell.

A quantum dot is a zero-dimensional electronic system, where quantum confinement leads to a density of states that is a set of delta functions. Within the effective mass approximation, the Schrödinger equation for an electron (hole) in a spherical well yields the energy spectrum E_{n,l} = (ħ²α_{n,l})/(2m*R²), where α_{n,l} is the n-th root of the spherical Bessel function of order l. The simplest model is an infinitely deep potential well. Taking Coulomb interaction (excitonic effect) into account, the energy of the photon emitted upon exciton recombination equals E_g + E_{conf}^e + E_{conf}^h - R_y*, where E_g is the band gap of the bulk material. Synthesis technologies (colloidal, epitaxial) allow obtaining dots with precise size control, and core–shell heterostructures improve quantum yield and photostability.

History

In 1981, Alexey Ekimov, while studying CuCl nanocrystals in silicate glass, noticed a blue shift of the absorption edge upon decreasing crystal size. In 1983-84, Louis Brus theoretically substantiated the quantum size effect in semiconductor nanocrystals, demonstrating the relationship between transition energy and particle radius. In 1993, Moungi Bawendi and colleagues developed a method for high-temperature synthesis of monodisperse CdSe quantum dots, paving the way for practical use. Subsequent research led to the creation of cadmium-free dots and applications in bioimaging and optoelectronics.

How it works

Quantum confinement: when the crystal size becomes smaller than the exciton Bohr radius, the motion of charge carriers is quantized. The Schrödinger equation for a particle in a three-dimensional potential well yields discrete energy levels, with spacing increasing as size decreases. Absorption of a photon creates an exciton, which then recombines radiatively. Due to the size dependence of the transition energy, quantum dots of the same composition can emit across the entire visible range. Spectral homogeneity is limited by the size dispersion of the ensemble, and blinking is associated with Auger ionization processes.

\hbar \omega = E_g + \frac{\hbar^2 \pi^2}{2 R^2} \left( \frac{1}{m_e^*} + \frac{1}{m_h^*} \right) - \frac{1.8 e^2}{4 \pi \varepsilon \varepsilon_0 R}

ħω — energy of the emitted photon, E_g — band gap of the bulk semiconductor, R — radius of the quantum dot, m_e^* and m_h^* — effective masses of electron and hole (less than the free electron mass), e — elementary charge (≈ 1.60×10⁻¹⁹ C), ε — dielectric constant of the material, ε₀ — electric constant (≈ 8.85×10⁻¹² F/m); the last term accounts for the Coulomb attraction of the exciton.

Open problems & fun facts

Suppression of blinking for stable single-photon emission; Creation of biocompatible dots for medical diagnostics and therapy; Scaling up the technology for electrically pumped quantum dot lasers

💡 Quantum dots can emit single photons on demand, making them ideal anti-bunching sources for quantum cryptography. Moreover, two dots never emit the same photon — this is used in quantum entanglement experiments.

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quantum dot

History

How it works

History

How it works

History

How it works

Open problems & fun facts

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