Sulfide Quantum Dot Band-Gap Comparator (2D)

Sulfide Compound

Nanocrystal Radius

Radius R 2.50 nm

Emission Color

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Live Readouts

Bulk gap E_g,0

2.42 eV

Confined gap E_g(R)

— eV

Confinement shift ΔE

— eV

Emission λ

— nm

Spectral region

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How it works

A metal-sulfide nanocrystal (CdS, ZnS, PbS…) confines its electron and hole to a sphere of radius R. Once R approaches the material's exciton Bohr radius, the band gap opens up above the bulk value — the Brus equation:

E_g(R) = E_g,bulk + (ħ²π²)/(2R²)·(1/mₑ* + 1/mₕ*) − 1.8e²/(4πε₀ε_r R)

The middle term is the particle-in-a-sphere kinetic-confinement energy (grows as 1/R²); the last term is the attractive electron-hole Coulomb correction (grows as 1/R, softens the shift). Emission wavelength follows λ = 1240/E_g(eV) nm. The plot on the right graphs this equation directly — E_g(R) computed live, not looked up — for the selected compound (or all three overlaid) across R = 0.5–10 nm, with the shaded band marking the visible range 380–750 nm converted back to eV.

CdS — bulk gap 2.42 eV (green), moderate effective masses (mₑ*=0.19m₀, mₕ*=0.80m₀), ε_r=5.7. Confinement pulls small dots toward blue/UV — the classic tunable QLED/solar-cell sulfide.
ZnS — bulk gap 3.68 eV, already in the UV. Even strong confinement (R≈1 nm) only pushes it deeper into the UV — used as a wide-gap shell material and UV phosphor, not for visible tuning.
PbS — bulk gap only 0.41 eV (mid-infrared), with tiny, nearly symmetric effective masses (mₑ*=mₕ*=0.085m₀) and a huge dielectric constant (ε_r=17.2). Its exciton Bohr radius is ~18 nm, so confinement is enormous — a few-nm PbS dot can be pulled all the way from the infrared into the visible, which is why it dominates IR photodetectors and near-IR bioimaging.

Pick a compound, drag the radius, and watch the marker slide along the real E_g(R) curve while the glowing quantum-dot disc recolors from the corresponding emission wavelength.

Selected material curve + marker Other materials (compare mode)