About Quantum Dot Emission
Quantum dots are nanoscale semiconductor crystals, typically 1–10 nm in diameter, whose optical and electronic properties differ fundamentally from those of bulk materials. The key phenomenon is quantum confinement: when a semiconductor crystal is smaller than the exciton Bohr radius, the electron and hole are physically confined in all three dimensions, quantising their energy levels. The result is a size-tunable band gap — and therefore a size-tunable emission colour.
This simulation implements the Brus equation (1984), the foundational model for quantum dot emission energy: E = Egap + ℏ²π²/(2μr²) − 1.8e²/(4πεε₀r). The first term is the bulk semiconductor band gap; the second is the kinetic confinement energy of electron and hole (scales as 1/r²); the third is the Coulomb binding energy between the electron-hole pair (scales as 1/r). At small radii the 1/r² term dominates, pushing energy up and wavelength down toward blue. At large radii the result approaches the bulk band gap.
The spectrum panel shows a Gaussian emission peak centred at the calculated wavelength, with width scaling realistically with quantum confinement. The dot panel shows the quantum dot drawn in its emission colour, with a simulated quantum yield glow. Three semiconductor materials are available: CdSe (visible range, the most studied), CdS (blue to UV), and ZnS (deep UV). A band gap offset control allows exploration of how defect states or surface chemistry shift the effective gap.
Frequently Asked Questions
What is the Brus equation?
The Brus equation calculates the emission energy of a quantum dot: E = E_gap + ħ²π²/(2μr²) − 1.8e²/(4πεε₀r). The first term is the bulk band gap, the second is the quantum confinement energy (which scales as 1/r²), and the third is the Coulomb attraction between the electron-hole pair. Smaller radius r means higher confinement energy and thus higher-energy (bluer) emission.
Why do smaller quantum dots emit blue light and larger ones emit red?
Quantum confinement restricts the motion of electrons and holes. Smaller dots have tighter confinement, which raises the energy levels (like a particle in a smaller box). The energy gap between the lowest electron state and the highest hole state increases as dot size decreases. Higher energy gap means higher photon energy, which corresponds to shorter wavelength — blue light. Larger dots have a gap closer to the bulk value, emitting lower-energy red photons.
What is quantum confinement?
Quantum confinement occurs when a semiconductor crystal is made so small (typically 1–10 nm) that its size becomes comparable to the electron's de Broglie wavelength or the exciton Bohr radius. At this scale, the continuous energy bands of bulk semiconductors split into discrete energy levels, like a quantum particle in a box. The energy of these levels depends on the crystal size, enabling size-tunable optical properties.
How are quantum dots used in LED displays?
QLED (Quantum dot LED) displays use quantum dots to convert blue LED backlight into pure red and green light. Because quantum dots emit at very precise wavelengths (narrow linewidth), they produce a wider color gamut than traditional phosphors. The exact emission color is set by the dot size, so manufacturers tune it precisely during synthesis. Samsung, Sony, and TCL use quantum dots in their premium display products.
What materials are commonly used for quantum dots?
The most studied quantum dots are cadmium selenide (CdSe), which covers the visible spectrum from ~480 nm to 650 nm depending on size. CdS dots emit in the blue-UV range, while ZnS (with a larger band gap) emits in the UV. InP and CuInS₂ are cadmium-free alternatives for biomedical use, as cadmium compounds are toxic. Perovskite quantum dots (CsPbX₃) are a newer class with very narrow emission linewidths.
How are quantum dots used in bioimaging?
Quantum dots serve as fluorescent labels in biological imaging because they are 10–100 times brighter than organic dyes, resist photobleaching, and can be tuned to emit at multiple wavelengths simultaneously. By attaching targeting molecules (antibodies, peptides) to their surface, quantum dots can be directed to specific cell structures. Near-infrared-emitting dots are especially useful for imaging through tissue.
What is the exciton Bohr radius?
The exciton Bohr radius is the characteristic size of the electron-hole pair (exciton) in a semiconductor, analogous to the hydrogen atom's Bohr radius. It is a₀* = ε·(m_e/μ)·a₀. For CdSe, a₀* ≈ 5 nm. When a crystal's size is smaller than a₀*, strong quantum confinement occurs and size-dependent optical effects become pronounced.
Why does the emission peak broaden in real quantum dot samples?
Real colloidal quantum dot samples contain dots of slightly different sizes (size dispersion). Each size emits at a slightly different wavelength, so the ensemble spectrum is a superposition of many narrow peaks, broadening the observed emission. Better synthesis control (narrower size distribution) produces narrower emission peaks — a key quality metric called FWHM (full width at half maximum), ideally under 20–30 nm for display applications.
What is the difference between Type-I and Type-II quantum dots?
In Type-I core-shell quantum dots (e.g., CdSe/ZnS), both the electron and hole are confined in the core material. The shell passivates surface defects and improves quantum yield. In Type-II heterostructures (e.g., CdSe/CdTe), the band alignment causes the electron and hole to reside in different materials. Type-II dots have longer excited-state lifetimes and can emit at wavelengths longer than either material alone.
Can quantum dots be made from non-toxic materials?
Yes. Cadmium-free alternatives include InP (indium phosphide), which covers the visible spectrum and is used in commercial displays; CuInS₂ for NIR emission; and silicon quantum dots, which are biocompatible and abundant. Lead-based perovskite quantum dots (e.g., CsPbBr₃) have outstanding optical properties but contain toxic lead, prompting research into lead-free tin and bismuth perovskite alternatives.