Nanotechnology & Quantum Confinement
Quantum Dot Artificial Atoms
Simulate 3D semiconductor quantum dots (QLED displays). 3D quantum confinement shifts the bandgap $E_g(R)$ via the Brus equation. Tuning dot radius $R$ from $2 \text{ nm}$ to $8 \text{ nm}$ shifts photoluminescence color from deep blue to bright red.
Emission Wavelength λ
485.0 nm (Cyan/Blue)
Effective Bandgap E_g
2.56 eV
Confinement Energy
+0.82 eV
Quantum Dot Setup
Visual Overlay
Controls
Brus Quantum Confinement Equation
Brus Bandgap Shift: E_g(R) = E_g,bulk + [ (ℏ² π²) / (2 m* R²) ] - [ (1.786 e²) / (4π ε₀ ε_r R) ]
Photoluminescence Wavelength: λ = h c / E_g(R)
3D Particle-in-a-Sphere: ψ_(100)(r) = [ 1 / √(2π R) ] · [ sin(π r / R) / r ]
Photoluminescence Wavelength: λ = h c / E_g(R)
3D Particle-in-a-Sphere: ψ_(100)(r) = [ 1 / √(2π R) ] · [ sin(π r / R) / r ]
Developer Reference
Core Algorithm & Standalone Script
// Quantum dot Brus equation confinement solver
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// E_g(R) = E_bulk + (hbar^2 * pi^2) / (2 * m_eff * R^2)