Shrinking Semiconductors
When a semiconductor crystal is reduced to a few nanometers, quantum mechanics rewrites its optical properties. Electrons and holes become confined in all three dimensions — like particles trapped in a tiny box — and their allowed energy levels shift upward from bulk values. This quantum confinement effect makes the effective band gap size-dependent, enabling precise tuning of absorption and emission wavelengths simply by controlling nanocrystal diameter during synthesis.
The Brus Equation
Louis Brus derived the foundational equation relating quantum dot size to its optical band gap in 1984. The confinement energy adds a term proportional to 1/r² (the particle-in-a-sphere kinetic energy) and subtracts a Coulomb attraction term proportional to 1/r. At small radii, the kinetic confinement term dominates, producing dramatic blue-shifts. The effective mass of electrons and holes in the specific semiconductor material determines how strong the confinement is for a given size.
Color from Size
A single material like cadmium selenide (CdSe) can emit every color of the visible spectrum depending on dot size. Dots with 1 nm radius emit blue light; 2 nm dots glow green; 3 nm dots shine yellow-orange; and 5 nm dots produce deep red. This size-color relationship is the basis of quantum dot displays (QLED technology), where three carefully sized dot populations create red, green, and blue subpixels with exceptional color purity and brightness.
Beyond Displays
Quantum dots are revolutionizing fields beyond consumer electronics. In biomedical imaging, their brightness, photostability, and narrow emission enable multiplexed tracking of different cellular processes simultaneously. In solar cells, multi-sized dot layers capture photons across the solar spectrum more efficiently than bulk semiconductors. As single-photon emitters, individual quantum dots are candidates for quantum communication and computing applications requiring on-demand photon sources.