// multi-utility computation suite · offline · instant · precise
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sci.quantum-dot-size-bandgap Calculator
Calculates the effective bandgap and emission wavelength of a semiconductor quantum dot from particle radius and bulk band structure. Brus equation: E_g(r) = E_g_bulk + h²/(8r²)(1/m_e + 1/m_h) − 1.8e²/(4πεε₀r) — Coulomb term slightly reduces confinement energy.
Inputs
D Nm
Distance across a circle through its centre. Always confirm units match the rest of the calculation.
Eg Bulk Ev
Reference formula or conversion factor shown for context.
M E Eff
Total mass (kg). Distinct from weight — weight = mass × gravity. Mass is constant; weight varies with location.
M H Eff
Total mass (kg). Distinct from weight — weight = mass × gravity. Mass is constant; weight varies with location.
Results
quantum dot bandgap Eg_QD (eV)
Sample size or count used in the calculation.
emission wavelength λ (nm)
The computed linear length.
confinement energy ΔE (eV)
Sample size or count used in the calculation.
ΔE = π²ℏ²/(2μd²)
Reference formula or conversion factor shown for context.
colour of emission
The colour classification or output colour code computed from the inputs.