The discussion below leans into technical language and uses terms commonly established in quantum mechanics and semiconductor physics.
Quantum dots are one of the clearest real-world examples of quantum mechanics at work. What if you could tune a material’s color just by changing its size? That’s the core idea behind quantum dots. Quantum dots are semiconductor nanocrystals typically a few nanometers in size, whose optical and electronic properties are governed by quantum confinement.
The diagram below illustrates quantum confinement in real space by comparing the quantum dot radius (rQD) with the exciton Bohr radius (rBohr). When the quantum dot radius is much larger than the Bohr radius, the electron–hole pair behaves like a bulk exciton, with its spatial extent determined primarily by Coulomb attraction and only weakly influenced by the dot boundary. As the quantum dot size decreases and becomes comparable to the Bohr radius, the exciton is increasingly distorted by the physical confinement of the nanocrystal. In the strong-confinement regime, where the quantum dot radius is smaller than the Bohr radius, the dot boundary dominates; the electron and hole are separately confined within the quantum dot volume, the exciton picture breaks down, and the wavefunctions are delocalized within the dot. The progression from larger (red) to smaller (blue) dots visually represents increasing confinement strength.
Figure 1. Real-space confinement.
The oscillatory wave shown inside the quantum dots above represents the spatial wavefunction of a confined charge carrier (electron or hole), not the wavelength of emitted light. In the strong-confinement regime, the physical boundary of the nanocrystal defines the allowed spatial modes, so only wavefunctions that “fit” inside the dot are permitted. This restriction raises the kinetic energy of the carriers, which ultimately manifests as a size-dependent shift in the optical emission.
This real-space confinement shows up directly in energy-space and leads the changes in the electronic structure. As the spatial motion of charge carriers becomes restricted, the allowed energy levels are no longer continuous, but become quantized.
Figure 2. Energy-space quantization.
The diagram above illustrates how electronic energy levels evolve from isolated atoms, to bulk materials, and finally to quantum dots. A single atom has discrete electronic states; when many atoms form a bulk crystal, these states broaden and merge into quasi-continuous valence and conduction bands separated by a band gap. In quantum dots, spatial confinement breaks these bands back into discrete, size-dependent energy levels. As the dot size decreases, the spacing between quantized levels increases, effectively widening the band gap. This size-dependent energy quantization explains why larger quantum dots emit at lower energies (red) and smaller dots emit at higher energies (blue), directly linking nanoscale confinement to tunable optical properties.
By controlling the size and structure, quantum dots can be engineered to emit pure colors across the visible spectrum. This tunability, combined with high brightness and narrow emission linewidths, has made quantum dots essential for modern display, lighting, photovoltaics, and bioimaging technologies.
That’s a good place to pause the ‘physics’ – if your brain feels a little warmed up, that’s quantum mechanics doing its job. In the next blog, we’ll switch gears to the ‘chemistry’ of quantum dots: the precursors, ligands, and reactions that turn simple salts into size-tunable nanocrystals. In future posts, we will discuss how the “materials in” strongly determines the “properties out”, and how Indium Corporation makes a difference in your properties out: not just the high-quality “materials in”, but also our technical know-how in these areas.
Indium, Our Product, Our Symbol, Our Name®.
Before you go, here’s a teaser question:
Which of the following compounds that Indium Corporation manufactures are used to produce quantum dots?
