The size of quantum dots (QDs) directly governs their energy absorption properties through quantum confinement effects, with smaller dots absorbing higher-energy light and larger dots absorbing lower-energy light:
1. Band Gap Tunability via Quantum Confinement
The exciton (electron-hole pair) becomes spatially confined when QD dimensions approach or fall below the exciton Bohr radius. This confinement increases the band gap, as described by the Brus equation:
Egap = Ebulk + (ħ2 π2 / 2μa2) – (1.8e2 / 4πεa)
where a is the QD radius, μ is the reduced mass, and ε is the dielectric constant. Smaller QDs exhibit larger band gaps, requiring higher-energy photons for absorption, while larger QDs absorb lower-energy photons.
2. Absorption Spectrum Shifts
- Smaller QDs (2.7–4 nm) absorb bluer light (higher energy), e.g., InP QDs with first absorption peaks at 2.7 eV (460 nm).
- Larger QDs (4–6.1 nm) absorb redder light (lower energy), e.g., CuInS₂ QDs show absorption onsets shifting toward ~1.7 eV as size increases.
3. Molar Absorption Coefficients
At energies far above the band gap (e.g., 3.1 eV), molar absorption coefficients scale with QD volume, implying size-independent absorption cross-sections per unit cell. Near the band edge, coefficients follow a power-law dependence on size:
εE1 ≈ 5208 · E1 · d2.45
for CuInS₂ QDs, where d is the diameter. For InP QDs, absorption cross-sections per dot grow with volume (∝ R3) at fixed photon energy.
4. Synthesis and Measurement Implications
Size uniformity critically affects absorption linewidths, as polydisperse samples show broadened spectral features. Advanced synthesis methods achieve ≤10% size dispersion in studies quantifying these effects.
Original article by NenPower, If reposted, please credit the source: https://nenpower.com/blog/how-does-the-size-of-quantum-dots-affect-their-energy-absorption-properties/
