Quantum Dot Calculator

Emission wavelength and bandgap from quantum dot size (Brus equation).

QD Radius (nm)

Bulk Bandgap (eV)

Effective Mass (m*/m_e)

Dielectric Constant

Tab to move between fields

Emission Wavelength (nm)

626.7

Effective Bandgap (eV)

1.98

Confinement Energy (eV)0.32

Coulomb Correction (eV)0.08

Color (1=UV...7=Red, 8=IR)7

Photon Energy (eV)1.98

Coulomb Ev0.08

How to Use This Calculator

Enter the quantum dot radius (nm) — smaller dots produce higher-energy (blue-shifted) emission.
Set the bulk bandgap (eV) and effective mass ratio (m*/m_e) for your semiconductor material.
Enter the dielectric constant for Coulomb correction accuracy.
Review emission wavelength (nm), effective bandgap (eV), quantum confinement energy, and Coulomb correction.
Use the color code output to correlate dot size with visible emission color for display or bio-imaging applications.

How the result changes with Bulk Bandgap (eV)

QD Radius (nm): Quantum dot radius. CdSe QDs: typically 1-5 nm.
Bulk Bandgap (eV): Bulk semiconductor bandgap. CdSe=1.74, CdS=2.42, InP=1.35.
Effective Mass (m*/m_e): Reduced effective mass ratio. CdSe~0.13, CdS~0.21.
Dielectric Constant: Relative permittivity. CdSe=10.6, CdS=5.7.

Identify Input Parameters
4 parameters
QD Radius (nm) = 3, Bulk Bandgap (eV) = 1.74, Effective Mass (m*/m_e) = 0.13, Dielectric Constant = 10.6 = 4 input(s) provided
Calculate Emission Wavelength
Emission Wavelength = emissionWavelengthM * 1e9
626.7 = 626.7
Calculate Effective Bandgap
Effective Bandgap = max(bulkBandgapEv, totalBandgapEv)
1.98 = 1.98
Calculate Confinement Energy
Confinement Energy = (h * h) / (8 * mEff * R * R) / e
0.321 = 0.321
Calculate Coulomb Correction
Coulomb Correction = coulombCorrection / e
0.082 = 0.082