LED Emission: How Band Gap Determines Color and Efficiency

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551 nm peak emission, 30 nm FWHM

With a 2.25 eV band gap at 300 K, the LED emits at 551 nm (green) with approximately 30 nm spectral width. At 20 mA with 70% IQE, radiant power is about 18 mW.

Formula

λ_peak = 1240 / E_g (nm)
FWHM ≈ 1.8 × kT (energy), converted: Δλ ≈ 1.8kT × λ² / hc
P_optical = IQE × EE × I × E_g / q

Electrons Become Photons

A light-emitting diode converts electrical energy directly into light through a quantum mechanical process: radiative recombination. When a forward-biased PN junction injects electrons into the conduction band and holes into the valence band, they recombine at the junction. In a direct-bandgap semiconductor, this recombination releases a photon with energy equal to the band gap. The relationship λ = 1240/E_g (nm) maps band gap energy directly to emission color — from infrared through every visible color to ultraviolet.

Spectral Width and Temperature

An LED does not emit a single wavelength. The spectral width arises from the thermal distribution of carrier energies around the band edges. The full width at half maximum (FWHM) scales with kT — roughly 1.8kT in energy terms, which translates to about 20–40 nm in wavelength for visible LEDs at room temperature. Higher temperature broadens the spectrum and red-shifts the peak slightly as the band gap shrinks.

Efficiency: From Electrons to Lumens

The wall-plug efficiency of an LED — optical power out divided by electrical power in — is the product of three factors: internal quantum efficiency (fraction of recombinations that are radiative), extraction efficiency (fraction of photons that escape the chip), and electrical efficiency (fraction of input power that reaches the junction). Modern blue GaN LEDs achieve IQE above 90% and wall-plug efficiencies exceeding 70%, making them the most efficient light sources ever created.

The White LED Revolution

White LEDs, which illuminate homes and streets worldwide, are typically blue GaN LEDs coated with a yellow phosphor (Ce:YAG). The phosphor absorbs some blue photons and re-emits them as broad yellow light; the combination appears white. This invention, which earned the 2014 Nobel Prize in Physics, has reduced global lighting energy consumption by roughly 40% and continues to improve as phosphor engineering and chip architectures advance.

FAQ

How does an LED produce light?

An LED emits photons when electrons in the conduction band recombine with holes in the valence band across a direct band gap. The photon energy equals the band gap energy, so E_g determines the emission color. This electroluminescence is far more efficient than incandescent emission because energy goes directly into photons rather than heat.

Why is band gap energy related to LED color?

The emitted photon wavelength is λ = hc/E_g = 1240/E_g (nm). A 3.0 eV gap (GaN) produces violet/blue light at 413 nm. A 2.25 eV gap (GaP:N) yields green at 551 nm. A 1.8 eV gap (AlGaInP) gives red at 689 nm. Infrared LEDs have even smaller gaps.

What limits LED efficiency?

Efficiency losses include non-radiative recombination (Auger, defect-mediated), light extraction losses (total internal reflection traps photons inside the chip), resistive heating, and current droop at high drive currents. The wall-plug efficiency is the product of internal quantum efficiency, extraction efficiency, and electrical efficiency.

Why do LEDs dim when they get hot?

Higher temperature increases non-radiative Auger recombination and shifts the emission spectrum. The internal quantum efficiency drops because thermal energy makes carriers more likely to recombine through defect states. This is why LED thermal management — heat sinks, thermal vias — is critical for maintaining brightness and lifetime.

Sources

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