Quantum Dots and Size-Tunable Color

Definition and physical basis

A quantum dot is a colloidal fragment of a bulk semiconductor — commonly CdSe, CdTe, InP, PbS, or cadmium-free InP/ZnS — small enough that its electronic structure differs from the bulk material. Absorbing a photon promotes an electron across the band gap, leaving a positively charged hole behind; the bound electron–hole pair is an exciton. In a bulk crystal that exciton spreads over a characteristic distance called the exciton Bohr radius (about 5.6 nm in CdSe, 18 nm in PbS).

When the crystal itself is smaller than that radius, the exciton is physically squeezed. Quantum mechanics then behaves like the textbook "particle in a box": confining a particle to a smaller box raises the spacing between its allowed energy levels. The band gap widens as the dot shrinks, so recombination of the electron and hole releases a higher-energy (bluer) photon. This is why the same chemical compound can emit anywhere across the visible spectrum simply by changing crystal size — a control knob unavailable to ordinary molecular dyes.

Quantum confinement — the governing effect

The physics is captured by the Brus equation (1984), which estimates the size-dependent band gap of a spherical dot of radius R:

E_gap(R) ≈ E_bulk + (h² / 8R²)(1/m_e* + 1/m_h*) − 1.8e² / (4πε₀εR)

The middle term is the confinement energy: it scales as 1/R², so it grows steeply as the dot shrinks and dominates the color shift. The final term is the Coulomb attraction between electron and hole, which scales as 1/R and lowers the energy slightly. Because m_e* and m_h* (the effective masses of electron and hole) are small in good confinement materials, even a modest change in radius moves the gap by tenths of an electron-volt.

Two consequences follow. First, emission is narrow — a well-made dot ensemble shows a fluorescence full-width at half-maximum of roughly 20–35 nm, far tighter than most organic dyes, giving saturated colors. Second, absorption is broadband: dots soak up every photon above the gap, so a single blue or UV source can excite red, green, and blue dots simultaneously. That combination — one pump, many pure colors — is exactly what displays want.

How they are made: hot-injection synthesis

The breakthrough that turned quantum dots from a curiosity into a material was the 1993 hot-injection method. A solution of coordinating solvent — classically trioctylphosphine oxide (TOPO), now often octadecene with oleic acid and oleylamine — is heated to around 250–320 °C under inert atmosphere. A room-temperature solution of precursors (for CdSe, a cadmium source such as cadmium oleate plus selenium dissolved in trioctylphosphine, TOP-Se) is then injected all at once.

The mechanics matter. The cold injection drops the flask temperature and triggers a single, brief burst of nucleation (LaMer mechanism): the monomer supersaturation spikes, thousands of tiny nuclei form nearly simultaneously, and the monomer concentration falls below the nucleation threshold. From then on the existing crystals only grow, so every dot experiences the same growth time — the key to a narrow size distribution (often <5%). Because color tracks size, chemists literally watch the reaction turn from yellow to orange to red and pull aliquots to "stop" at a chosen wavelength. Surface ligands (long-chain carboxylates, phosphines, amines) cap the dots, prevent fusion, and keep them dispersible in nonpolar solvents.

Older aqueous routes and glass-melt methods (Ekimov's original doped silicate glasses) also produce dots, and greener InP-based syntheses have grown to sidestep toxic cadmium, but hot injection remains the benchmark for optical quality.

Core–shell structures and quantum yield

A bare CdSe core has dangling bonds and surface trap states that let excitons recombine non-radiatively — as heat rather than light — so raw cores often fluoresce weakly. The fix is a core–shell architecture: growing a thin epitaxial layer of a wider-band-gap semiconductor, most famously ZnS or CdS, around the CdSe core (Hines and Guyot-Sionnest, 1996; Peng and coworkers). The shell forms a Type-I energy well that confines both electron and hole to the core and passivates surface defects.

• Photoluminescence quantum yield — the fraction of absorbed photons re-emitted as light — jumps from a few percent for bare cores to 50–90%+ for good CdSe/ZnS dots.
• Photostability improves dramatically; shelled dots resist photobleaching far better than organic dyes, staying bright through millions of excitation cycles.
• Blinking (random on/off fluctuation of single dots) is suppressed by thick or graded "giant" shells.

Because ZnS has a larger lattice mismatch with CdSe, intermediate CdS or gradient shells are often used to relieve interfacial strain and avoid cracks that would reintroduce traps.

Applications — why quantum dots matter

Displays. The largest commercial use is in QLED and quantum-dot-enhanced LCD televisions. A blue LED backlight passes through a film of green- and red-emitting dots; the pure, narrow emission expands the color gamut to cover a large fraction of the Rec. 2020 standard, giving richer reds and greens than white-LED phosphors. Electroluminescent QLEDs, where dots emit under an applied voltage, are the next generation.

• Bioimaging. Water-solubilized dots serve as ultra-bright, photostable fluorescent labels for tracking proteins and cells; their broad absorption lets one laser excite many colors at once for multiplexed imaging.
• Solar cells and photodetectors. PbS and PbSe dots absorb in the near-infrared and are solution-processable, enabling low-cost, tunable-gap photovoltaics and IR sensors.
• Lighting and lasers. Dots down-convert blue or UV light for warm-white LEDs and act as low-threshold gain media.

The recurring theme is the same: a single, cheap, solution-processed material whose optical properties are dialed in by controlling crystal size during synthesis.

A brief history

In 1981 Alexei Ekimov, working in the Soviet Union, noticed that copper chloride and cadmium selenide nanocrystals grown inside colored glass shifted their absorption with particle size. In 1983 Louis Brus at Bell Labs saw the same size dependence in colloidal solution and, in 1984, derived the effective-mass "Brus equation" that quantified quantum confinement. The chemistry lagged the physics until 1993, when Moungi Bawendi's group at MIT (with Murray and Norris) published the hot-injection synthesis of monodisperse CdSe. Core–shell passivation (mid-1990s) and greener, cadmium-free formulations followed. The story closed a loop in October 2023 when Ekimov, Brus, and Bawendi shared the Nobel Prize in Chemistry.

Approximate CdSe quantum-dot size vs emission color

Diameter (nm)	Emission wavelength	Color	Band gap (eV)
~2.0	~480 nm	Blue	~2.6
~3.0	~530 nm	Green	~2.3
~4.5	~590 nm	Orange	~2.1
~6.0	~640 nm	Red	~1.9