A semiconductor nanocrystal a few nanometers across that confines electrons and holes in three dimensions. The confinement energy is roughly inversely proportional to the square of the size, so the emission wavelength can be tuned by size.
Japanese name: 量子ドット
Quantum dot appears in 3 practice questions across 2 topics, including Thin films, surfaces and nanomaterials, Nanomaterials.
Field: Nanomaterials
When a semiconductor crystal is made a few nanometers across, comparable to or smaller than the extent of an electron–hole pair (an exciton), the electron and hole behave as waves confined in a small box and their energies take discrete values. Even the lowest level is raised by the confinement energy, so the effective band gap becomes larger than in the bulk and smaller particles emit shorter wavelengths of light. Tuning the emission color by changing only the size of the same material is the defining feature, and the 2023 Nobel Prize in Chemistry was awarded to three researchers for discovering this effect and establishing methods of synthesis.
The lowest energy of a particle confined in a spherical box of radius R is ħ²π²/(2m*R²), where m* is the effective mass, so it is inversely proportional to the square of the radius and larger for a smaller effective mass. Adding the contributions of both electron and hole and subtracting their Coulomb attraction gives the estimate known as the Brus equation. Confinement acts strongly when the radius is comparable to or smaller than the exciton Bohr radius (about 5 to 6 nm for CdSe). Below a few nanometers, however, the bands depart from parabolic shape, so the relation between actual size and gap is usually read from a calibration curve built from measurements.
Quantum dots include colloidal quantum dots, synthesized in solution with surfaces covered by organic molecules (ligands), and self-assembled quantum dots, which use island structures that form during crystal growth. The latter use Stranski–Krastanov growth, in which a film on a substrate with a different lattice constant turns into islands, and are used in systems such as InAs/GaAs for semiconductor lasers and single-photon sources. On the other hand, although gold and silver particles are also nanometers in size, their colors come from collective oscillations of surface electrons (plasmons), a phenomenon separate from the confinement effect of quantum dots.
Many of a quantum dot's atoms are at the surface, so when surface defects trap electrons or holes, energy is lost without emitting light. The CdSe core is therefore wrapped in a shell of a wider-gap material such as ZnS, a core–shell structure that raises emission efficiency and stability. In displays, quantum dots are used in color-conversion layers that turn the light of blue LEDs into red and green, and their narrow emission widens the range of reproducible colors. Because cadmium is a restricted substance, replacement by quantum dots with InP cores is advancing, and applications as fluorescent labels in biology and in solar cells are also being studied.
Answer: C. The band gap becomes larger and the emission shifts to shorter wavelengths (toward blue)
When the particle size becomes comparable to or smaller than the exciton Bohr radius, a measure of the spatial extent of the electron and hole (about 5–6 nm for CdSe), the carriers are confined in a small space and the energy levels become discrete and more widely spaced. This is the quantum size effect: the smaller the particle, the larger the effective band gap, and the emission shifts to shorter wavelengths (toward blue). The emission color of a single material can therefore be tuned just by changing the size, which is used for color conversion in displays. The choice saying the gap gets smaller is the reverse. The same color as the bulk is obtained when the particles are much larger than the Bohr radius.
Answer: B. About 2.42 eV
The confinement energy is proportional to 1/R², so going from R = 3.0 nm to 2.0 nm multiplies it by (3.0/2.0)² = 2.25, giving 0.30 × 2.25 = 0.675 eV. The effective band gap is 1.74 + 0.675 ≈ 2.42 eV, corresponding to an emission wavelength of roughly 1240/2.42 ≈ 513 nm (green). At R = 3.0 nm it is 2.04 eV (about 608 nm, orange to red), so smaller dots emit at shorter wavelengths. About 2.19 eV assumes proportionality to 1/R, and about 2.75 eV to 1/R³. In real quantum dots, the effective mass approximation breaks down at small sizes (band nonparabolicity), and the confinement energy usually increases more gently than 1/R², so this value is only a guide.
Nanoparticle is a broad term for any particle about 1 to 100 nm in size. Quantum dots are those, mainly semiconductor nanocrystals, whose energy levels and band gap change with size through the confinement of electrons and holes. Even the same substance is not called a quantum dot if it is too large for confinement to act.
Mainly the material and the particle size. The material sets the approximate position of the bulk band gap, and the smaller the particle, the more confinement widens the gap and shifts emission toward blue. The more uniform the sizes, the narrower the emission, and the type of shell and the surface state also affect small wavelength shifts and emission efficiency.
When light, heat, oxygen or moisture oxidize the surface or strip off ligands, defects increase and emission efficiency falls. Besides wrapping them in shells, quantum dots are therefore sealed in polymers or glass, or sandwiched between films that block oxygen and water. Ensuring stability is said to be more difficult for cadmium-free materials.
In real quantum dots, the effective mass approximation breaks down at small sizes (band nonparabolicity), and the confinement energy usually increases more gently than 1/R², so this value is only a guide.
For CdSe quantum dots (bulk band gap 1.74 eV), assume a sim…The self-assembly of quantum dots of InAs on GaAs (lattice mismatch of about 7%) is the classic example.
Among thin-film growth modes, which correctly describes Str…Quantum size effect Stranski–Krastanov growth BET method Bottom-up synthesis Carbon nanotube Graphene Melting point depression of nanoparticles Specific surface area Zeta potential