• Estimate the ground-state binding energy of a three-dimensional hydrogenic Wannier-Mott exciton from reduced electron-hole mass and dielectric screening.
• Compare fabrication or device scenarios while holding coefficients and unit conventions constant.
• Check a hand calculation before moving to a higher-fidelity process, circuit, or TCAD model.

Binding energy grows linearly with reduced mass and falls with the square of relative permittivity. The unscreened εr = 1 case is mathematically valid, and the model does not impose an artificial upper bound of one on µ/m0.

• The result assumes isotropic parabolic bands, a bulk 3D Coulomb potential, and spatially uniform dielectric screening. Two-dimensional materials, nonlocal screening, mass anisotropy, central-cell effects, polaronic screening, and uncertainty over static versus optical permittivity can produce non-hydrogenic binding energies.
• Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.

• Varshni Bandgap

  Estimate the host semiconductor's temperature-dependent band gap; exciton binding is a separate correction between the quasiparticle gap and an excitonic optical transition.

• AlGaN Bandgap

  Estimate an AlGaN alloy band gap from composition; use this tool instead for the electron-hole Coulomb binding within the stated hydrogenic model.