About Quantum Dots — Size-Tunable Fluorescence
This simulation visualises quantum confinement in semiconductor nanocrystals (modelled as CdSe). Each dot absorbs ultraviolet light and re-emits a single visible photon whose colour depends only on the crystal's radius. The emission energy follows the Brus equation, E = E_bulk + (ℏ²π²/2r²)(1/m_e* + 1/m_h*) − 1.8e²/(4πε₀ε_r r), with the emission wavelength obtained from λ = hc/E, computed live in SI units.
The Dot Radius slider (1.5–4.5 nm) is the key control: shrinking the dot raises the confinement term, which scales as 1/r², blue-shifting the emission from red toward blue. Number of Dots, Temperature and UV Intensity govern how many crystals are shown, their thermal jitter and excitation rate. Such tunable emitters underpin quantum-dot displays, LED lighting and biological fluorescent labelling.
Frequently Asked Questions
What is a quantum dot?
A quantum dot is a semiconductor nanocrystal, typically 2–8 nm across, small enough that its charge carriers are confined in all three dimensions. This confinement quantises their energy levels, so the dot behaves almost like an artificial atom whose optical properties depend strongly on its physical size.
Why does the colour change with size?
As the radius r shrinks, the confinement energy grows in proportion to 1/r², widening the effective bandgap. A larger gap means each emitted photon carries more energy, and since λ = hc/E, the emission wavelength becomes shorter. That is why small dots glow blue and larger dots glow red.
What is the Brus equation?
The Brus equation estimates a quantum dot's emission energy as E = E_bulk + (ℏ²π²/2r²)(1/m_e* + 1/m_h*) − 1.8e²/(4πε₀ε_r r). The first term is the bulk bandgap, the second is the kinetic confinement energy of the electron and hole, and the third is the Coulomb attraction between them.
What do the four sliders do?
Dot Radius (1.5–4.5 nm) sets the confinement and therefore the emission colour. Number of Dots (4–30) changes how many nanocrystals appear. Temperature (100–600 K) controls their thermal jitter, and UV Intensity (0.1–1) sets how often the dots are excited and emit photons.
What material does the simulation model?
It uses parameters for cadmium selenide (CdSe), a classic quantum-dot material. The constants include a bulk bandgap of 1.74 eV, an electron effective mass of 0.13 m_e, a hole effective mass of 0.45 m_e and a relative permittivity of 10.6, all fed into the Brus equation.
Is the simulation physically accurate?
The energy and wavelength calculations use the real Brus equation with literature CdSe constants, so the colour-versus-size trend is faithful and quantitatively reasonable. The animated dots, photons and UV beams are stylised for clarity, however, and the model omits effects such as surface traps, size dispersion and the Stokes shift.
What is the Coulomb term for?
The final term, −1.8e²/(4πε₀ε_r r), accounts for the electrostatic attraction between the confined electron and hole, which together form an exciton. It slightly lowers the total energy and grows as the dot shrinks, partially offsetting the kinetic confinement term.
Why is UV light used to excite the dots?
Ultraviolet photons carry more energy than the dot's bandgap, so they can lift an electron across it and create an excited exciton. The dot then relaxes and re-emits a lower-energy visible photon. This down-conversion from invisible UV to bright visible colour is what makes quantum dots so striking under a UV lamp.
What does temperature change in the model?
Raising the Temperature slider increases the random thermal motion of the dots and modestly boosts the photon-emission rate shown in the statistics bar. In this simplified visualisation temperature does not shift the emission colour, although real dots do show a small temperature-dependent bandgap change.
Where are quantum dots used in the real world?
Quantum dots power QLED televisions and monitors, where size-tuned dots produce pure red and green light for wide colour gamuts. They also serve as fluorescent tags in biomedical imaging, as down-converters in LED lighting, and as active materials in solar cells and emerging photodetectors.